Ok, my store with cheap aliexpress watches was not a great success, so I finally decided on a general store and I have one more variable in my pocket, which is the ability to test products.
I've started in Poland, however I'm going to make the second step in the USA. The only problem is that I have only one payment gateway - PayPal and others doesn't seem to agree me for now. Any suggestions for payment providers with easy way to acceptation? I also tried Skrill but they haven't answered yet.
1. Website:
I don't test this product. It's just to show you how the website looks.
Single product - mobile - there are Reviews imported from Aliexpress (they haven't been imported in english version yet), so I decided to create the second (Add To Cart/Buy now) buttons on the bottom to give people a possibility to buy after reading reviews and they don't need to scroll up again.

Single product - desktop:

Checkout mobile - I've decided to remove all unnecessary fields - even phone number. I've also looked into Hotjar recordings and saw that when somebody enters checkout, he firstly scroll down to see if everything is okay in the order summary, so I moved this summary to the top of checkout (it's by default above Payment Gateways below checkout form). Also when you write address in the "Street address" field it uses Google Maps autocomplete and when you choose any address - it fills automatically other fields like City and Zip Code.

Checkout desktop:

Advertising:
I started with PPE campaigns. Each campaign for one product. Each campaign had 4x ad set but with different audience targeting to check which one is the best. Budget of each ad set was $6p/d. Each ad set had 3x the same ad inside.
After one day, I've chosen the product and 3 ad sets of this product that had CTR over 1.5% or at least one add to cart event.
Then I've made transition to WC with 3 best audiences and used optimization for Purchase event.
So in campaign were 3 ad sets, each with budget $10p/d, each with 7-day click optimization and each with the placement set to Facebook Feed.
Unfortunately all 3 ad sets in my campaign spent only $0.3 during 24 hours. I didn't know what happens, so asked on Facebook chat and they said my audiences probably are similar and I need to exclude others in each one.
Ok, so I run campaign for another day with better prepared audiences and... the same, still spent around $0.3.
I asked Facebook again - this time they said to use Automatic Placements - not just Facebook feed. Ok, I did it and in the next day still the same. Almost nothing spent.
Finally somebody in Facebook checked my pixel and told me that I don't have enough data to run Purchase event. I've changed optimization event to Initialize Checkout where I had some more pixel data (67) and YEAH - it started to spend money. 
As we can see, you need at least 50 Purchase data in pixel to run optimization for this event. Probably the same for others. The best thing is that even Facebook support isn't sure about this.
I'll keep this thread updated how it's going. I don't have much statistics for now, because I've just figured out why Facebook didn't want to spend my money.
Please let me know if you have any suggestions to all of it.
Thank you!
Hey glad to see you're still working at it I'll be following and good luck!
Yeah, I had some failures but I still work and learn more and more. I've never even thought to stop.

Just to keep you updated.
I've tested some products in the USA - each product tested in 4 different audiences.
Each audience $6p/d.
Audience size: 800k-1.5mln.
Testing time: 1 day.
I decided to make transition to WC if there is around 1.5% CTR or at least 1ATC after one day. Do you think it's okay?
Unfortunately I haven't achieved even 1% CTR or ATC on any product / any audience.
I'm thinking about making more targeted audiences with around 300k people. I thought that maybe smaller audiences will generate some sales. What do you think? I know that bigger audiences should generate more profit in the long term, however I'd like to achieve break-even or small profits to feel better. 
Any ideas/types of products that are easy to sell for the beginner?
Yes, there are many ideas and product that are easy.
But none of them involve dropshipping through a general ecom store and Facebook
Really glad to see you're not giving up!
How many products have you tested? You'll need to test lots. Try testing 1-3 per day.
Are you going niche or general? In either case, do some research to find out what the best sellers are right now. Go to big ecom sites and see which products are featured in a prominent place (top of homepage typically, or in the "best-sellers" category/page).
As for targeting, if you're going niche then obviously try to target niche (if you could reveal your niche maybe we can provide some suggestions). If you're going broad promoting general merchandise that you feel enough of the general audience would be interested in, still try to limit your targeting if possible. If not, you can still at least see which age group and gender convert best, but that would only be possible after quite some spend to collect enough data on purchases.
And the dropshipping model, as the very experienced pekadis has pointed out, really isn't great for profits. User acquisition cost is typically the highest, and if you can't sell to the same customer base again and again then you'd be 1)leaving lots of money on the table, 2)limiting profits to whatever you can make from just that initial (and the only ever) sale, 3)limiting how high you can bid for traffic due to the limited amount of profits you'd be making. But one step at a time I guess - for now you need to find at least a couple of products that sell well enough that you'll have something to experiment other tactics with.
Amy
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Thanks for your advices! They created a lot of questions in my mind.
This is general store. I've tested six products for now but I'm not sure if I tested them properly.
1. What kind of products should I choose? Sometimes I see nice product but I think that this has been sold so many times on Aliexpress that probably all people I'd like to target have seen it at least several times.
I wonder, isn't it too late for me to start to promote the product if it's in the featured/best sellers section in big stores?
Do they use the trick by putting new products in those places for better testing?
I know some products that probably are winners but I've seen so many ads with them that I didn't even try to test them, because I think the market is oversaturated. I'm not sure if it's a good thinking from my side.
2. I've tested all products in Poland and the USA using PPE campaigns. Each product with 4 different audiences, so finally I needed to spend $24 per product to test. It's a little lot of for me.
a) Do I need to test each product in 4 audiences? Maybe it's better to just target one that seems to be the best and test other audiences when I know a product is the winner?
b) I've used PPE, because I watched some general store tutorials and they said to test PPE firstly. However, it doesn't seem to be a good idea for me, because I'm getting a lot of likes and shares but only 3-5 people enters my website. In fact it looks I spend $24 for PPE (with 4 different audiences) and I don't have a big chance that somebody will buy a product. I just have some data but I'm not sure if it's even accurate when it looks like:
Ad set 1: 1 click
Ad set 2: 0 clicks
Ad set 3: 1 click
Ad set 4: 3 clicks
I see that Ad set 4 is the best but it could be just a coincidence.
But ok, I chose "the best" ad set and started WC campaign to see how it works (I didn't do it with other products, because they had even worse statistics in CTR). I spent $10 and it generated 15 visits on my website and also a lot of likes. Unfortunately no Purchase.
Do you think I should start testing using just WC (without PPE on the beginning)?
3. How much money should I spend to test each product? It seems to me that 4 * ad set * $6p/d = $24 is a lot of for a single product and I would need to have a big budget to test i.e. 3 products daily. How to cut testing costs?
4. When do you know that product is the winner? How much do you usually spend for testing? Does it need to be a profitable (break-even) product campaign to say that product passed test?
5. You said dropshipping in this model isn't good for profits. I'm not sure what you mean, because it looks that we see everywhere something like: "Dropshipping is better than ever before", "E-commerce is the best idea for marketers in 2018" and so on.
Do you mean I need to collect the client base and force them to enter my store yourself, even without any advertisement to have real profits?
I know the website called joom.com that has really, really cheap products, sometimes even cheaper than you can find on Aliexpress. It looks they advertise on Facebook not to sell something but to collect leads and their application installs to retarget (using push or something) an infinite number of times. Is it the model we should aim to have real profits? Or maybe you meant something like affiliate store with other traffic source than Facebook? Can you develop a little? I've wasted some time and money working on not the best business models and would like to focus on something profitable finally. 
I know it's a little long post but I will be very grateful for any advices.
Thanks!

@amy / vortex is giving some great advice here.
Especially when it comes to testing.
If you do want to go the general store route, focus on testing products.
I have mentioned this before, but use a proven ad template and then just keep testing products.
Don't go by intuition. Just as with the watches, it's very hard to guess what will work. And you are not alone there. I have misjudged products before too, underestimated and overestimated demand.
So what you want to build is a testing machine.
No focus on the site itself, but on the process, the ads and products.
Look to build your audience on RFM, recency, frequency and monetary. This is the tested method of the direct response copywriters of the old days.
So build audiences based on:
recency - how long ago they purchased
frequency - how often they have bought
monetary - how much they have spent
Ideally, you want to focus on people who bought very recently (they are likely to buy again, buy often (have a low threshold to buying something), and spend a lot (this is relative to the others).
By segmenting your audience that way, you build up something very valuable.
Good luck