(If you didn't know - I'm from Poland)
I don't see a reason why driving in Poland would be a bad idea, except maybe road holes and AFAIK expensive and rare highways. There's no highway on the way from Vilnius to Warsaw (but my city might be there - there are two sensible ways through the border ), but at least there's an express road for about a third of that way (free, 100/120km/h limit, 2 lanes in each direction, sometimes divided by barriers, sometimes not). I see that it's similar on the way from Warsaw to Kraków. From Kraków to Poznań you can go about 2/3 of the way using highways - first a bit of A4, then from Piotrków Trybunalski A1 and A2.
Traffic in Warsaw is dense...
...and I checked - Warsaw in some rankings is one of the most congested cities in the world. Oops.
It's safe to drive... anywhere, I'd say? IDK, maybe I'm wrong, but I can't think of a place in Poland where it would be unsafe to just drive. Unless you mean roads so badly designed/built that it's easier to have an accident - then sure, you'll find some. About leaving car... I'd say keep away from the stadiums and maybe worse looking residential areas and your car will be fine.