interesting that usta means both mouth and lips - what about warga for lips and buza for mouth (as in daj mi buzy)
"warga" is one lip, "wargi" is plural. But that's... a bit technical. Not used that often. You can for example say "Ugryzłem/am się w wargę" (I bit myself on the lip), but in most situations, "usta" are used. Even about applying lipstick we would rather say "Kobieta maluje usta", not 'wargi'. Although of course she applies lipstick exactly on her lips.
"buzia" is the word you mean, you need the palatalized 'z'. It's correct, but it's rather childish register. So "Daj mi buzi" will work for "Give me a kiss", but either that would be childish-romantic talk, or more probably (I think) a kiss on the cheek between members of family.
"Usta" is pluralia tantum, so if anything, it would be "twoje/wasze" and preferably "swoje". But whose mouth would you open rather than your own? We won't use any pronoun here because the situation seems obvious. If by any chance you really had to open someone else's mouth, then you would specify it.
"twoje/wasze/swoje" are among accepted options as technically they are correct, but using them does not sound that natural.