Будинок і дім - They seem very similar to the Polish "budynek" (building) and "dom" (house).
I think "Where is my budynek?" could mean "Where is my house?" if you live in an apartment building, but not if you live in a bungalow or detached home, for instance. Is it the same in Ukrainian, or can будинок always mean "house"?
Будинок ususally means house or building, while дім usually means home (but can sometimes be also used to mean house)
"Це" can be declined: "ця, цей, ці, ...," similar to "this" and "these" in English. "Де" has only one form, like "what."
It seems like це is pronounce like "say" and де is pronounce like "day". That's how I remember them.
This of course is a very useful question when totally drunk. Thanks, Duolingo!
Why у has a u sound when after б?
Budýnok is from Polish budynek, it's borrowed from Middle High German 'būding', probably from the same root as 'bauen' (to dwell, live).