"Do you love me?"
No, because you used Accusative twice.
If you want to use singular 'you' you could say: Kochasz mnie? Czy mnie kochasz? Czy ty mnie kochasz?.
Not really. Only if it would make sense to say "What?! You love ME?!" and then you need to strongly emphasize 'mnie' with your voice. And even then it could make more sense to just emphasize "mnie" in normal "Kochasz MNIE?!"
The correct answer that was shown to me was Ty mnie kochasz. Since I thought that pronouns could be dropped, I had written mnie kochasz. My question: Does the word order change when you drop the pronoun? Thanks.
Not exactly, but the thing is, that this sentence is just three words long. And putting the personal pronoun (in a function other than the subject of the sentence) at the beginning of the sentence is weird on the border of just wrong.
In this particular sentence, the only really natural question is "Kochasz mnie?" (and "Kochacie mnie?" if you really feel the need to ask it in plural 'you').
Then, you can of course use the question-making "Czy", and then it feels a lot better if you specify the subject: "Czy ty mnie kochasz?" is definitely better than "Czy mnie kochasz?". "Ty mnie kochasz?" definitely looks like a surprised "What?! You love me?!". And "Mnie kochasz?" is just too bad to accept.
So what's the difference between "Kochasz mnie?" And "Kochacie mnie?". I've always used the former with my husband - jokingly asking if he loves me.
And you could use the latter with his parents :) The second one is plural. Polish distinguishes between singular and plural 'you', unlike English.