the specific question about requirements for my residency.
You need two things (prior to 31/12/20 when it changes). These are:
- A meldunek. This takes a few minutes at the town hall. You need to fill a form in, show your passport, and the owner of wherever you live shows proof of ownership.
- Health insurance. You can either use the NFZ or private. The type you need doesn't cost as much as you mention.
Then you go to the regional office that issues residency with proof of those two things, fill in a simple form and wait for your card.
Note that this is the system prior to the end of 2020 (after which you will probably need to convert the card they give you to a new one. If you leave it until 2021 it is very possible that you'll need to go through a far lengthier procedure depending on whether there's a Brexshit deal or not and depending on what the Schengen zone and Poland decide to do.
There are several facebook groups where this is much discussed. I don't use FB myself, however a quick look at a friend's shows groups called Brits in Poland, Brytyjczycy w Polsce and various variants of those. People in those groups are going through the process and can advise in real time.