I wanted to ask about receiving healthcare in Poland. Do they have something similar to the NHS there? Or similar to Medicare in Australia? And if so, being an EU citizen would I qualify for it? Bear in mind it is about 3 years since I have even been in Europe.
Yep, there's something called the NFZ. It operates slightly differently to the NHS - many places will be both NFZ and private, so you have to ensure that you're being treated under the NFZ scheme and not privately.
But you won't qualify automatically...
The UK NHS won't be covering you anymore, as you will have lost residence in the UK.
If they do, how much does it cost? And is private health cover/insurance expensive?
It's cheap for me, but it depends on your age. medicover.pl is your friend in this respect for health care.
Public health care is funded via something that you'll grow to hate called ZUS - which is basically a horrifically high social tax that goes to pay pensions and health care. But be warned, the system is very awkward - residence alone doesn't give you NFZ cover (unlike the UK NHS), although there are apparently ways to get round the requirement to actually pay ZUS a penny.