I'd agree that Polish is difficult, but it's not unlearnable.
Before even thinking about cases, it's probably best to forget all about the "a" and "the" in English to give yourself a chance. (A background in Latin would be quite helpful.)
I've just returned from the most wonderful time in Kraków and my limited Polish took me a long way. I didn't have to use English at all in the hotel.
Outside, I used Polish about 80 per cent of the time...most difficulties came when I was speaking to older people who tried to engage me in a fuller conversation after I'd asked them for directions.
Younger people were as keen to use their English as I was to use my Polish, so a lot of conversations were conducted in my often-rubbish Polish and their sometimes-questionable English.
It doesn't matter. We communicated perfectly, and I never got lost.
I do so much wish that I'd been able to give the older folk, who'd no English, a better conversation, but I hope to improve on that next time around.
As an example, a waiter in a bar used the word "podać several times. I didn't realise, at first, that it was a "dać" with extra meaning...
And that's the beauty of Polish. Just when you think you can say "barszcz" correctly, you find that a simple verb like "jehać" can take on many different meanings when you put "po" or "do" or "wy" in front of it.
I look forward to going back to Poland.
Your language is beautiful and your people are a pleasure.
However:
A general Celtic “r” is much closer to one I’d find normal.
Not quite so sure I'd agree with the concept of a general Celtic "r". Welsh does have a trilled "r" and Scots Gaidhlig does too, but in Irish (my native language) you'll only find it among old people with no teeth. I'm not denying that it was there (it was until about two generations ago), but it's very hard to find nowadays. Sadly, in my opinion.
An excellent point though, because the Welsh sound answers "r" in "herbata" quite closely.
Ian
What is the most annoying thing about non-native Polish speakers?
Their teeth?