When I've looked at academic language comparisons, Polish, Russian, and Ukrainian are all about the same distance from each other. Somewhere in the range of distances of Portuguese/Spanish/Italian, which have lots of very similar words. A single word isn't going to get somebody in trouble, but a sentence? Going to raise eyebrows, and likely capture unless you've got people to vouch for you being a patriotic newly Russian citizen, just trying to catch up to the new reality. The areas that are currently occupied, as well as Russian lands that border Ukraine, have a mixed vernacular called Surzhyk, which uses Ukrainian sounds and grammar but lots of Russian vocabulary and idioms.

Early on in the occupation, one form of resistance was simply graffiti with a letter that's in the Ukrainian alphabet that's not in the Russian alphabet, like ї. That sort of symbolic resistance has been replaced entirely by far more strategic resistance these days, according to recent reporting.

No it won't.

Honestly, this is like saying that someone who speaks Italian would mistake your for speaking Spanish. That's how it sounds. If you disagree - you clearly don't speak both languages. Just because some words are similar doesn't make them sound same.