So, "Gnu is Not Unix, Dawg"?

“Pies” is Spanish for feet, which was my second reading after seeing the pronunciation. The first was in reference to round baked deserts.

Is that pronounced “peace” or “piss”?

More like pi+[y]es, but single syllable and no y.

EDIT: Here are three audio files to hear: https://pl.wiktionary.org/wiki/pies#pies_(j%C4%99zyk_polski)

As an American, I hear “pyes” - a single syllable “yes”, with a preceding “p.”

When do you use that vs собака (sobaka)?

I don't, I'm Polish. Can't say for sure for Ukrainians, don't know Ukrainian that well, but my reading of https://en.wiktionary.org/wiki/%D1%81%D0%BE%D0%B1%D0%B0%D0%B... and https://en.wiktionary.org/wiki/%D0%BF%D0%B5%D1%81#Ukrainian suggests that пес must be male, but собака is either male or female. I might be wrong.