The sleep in the woods thingy sounds good. I would not light a fire, except if there is a firepit and you can easily control it. Bush fires are no joke. Again, my recommendation is to find a place where it is legal to light a fire, but you can do without. It's just more fun (to me).

Here is an interactive map that shows all firepits in Poland (generated from OSM). Some might be at campsites, but some are in the wilds as well.

I must confess that I never slept in a hammock outdoors, so I can't give suuuper good advice on that. A friend of mine is always putting her sleeping mat in the hammock, and sleeps in a sleeping bag on it. There are special underquilts for hammocks, but that is pricy. Be aware that if you have no mosquito net, there is nothing that protects you from them. I don't know whether they are a problem in Poland, but just saying. Same goes for tarp. If you have no tarp, you have 0 rain protection, so you must be sure that there won't be rain.

Some people like the 'laying under stars, so close to nature' thing, others feel more exposed and safer in a tent. Ultimately, only you can tell. A hammock can be very fine.

The birch forest near the road sounds great! Close to your car is a good idea.

You don't have to, but I would be interested in your updates (especially if you do sleep outside)!