Good question. I would like to be sure what I've read in the tips and notes works here:
"you may recall that mass nouns may be used in Gen. instead of Acc. if you mean "some quantity": Купи́ сы́ра/карто́шки."
So would "... slice some bread" be translated as "... хлеба и сыра"?
It does not drop pronouns frequently.
And it is not OK to drop them anywhere, only in some cases it is OK to drop them (unlike for example Spanish, where pronouns are omitted very often, and it is almost always OK to do so if you like).
I've seen very similar sentences (a positive one, and the exact equivalent negative sentence) such that a native speaker confirmed here on Duolingo that it is OK to drop the pronoun in one of them, but unacceptable to do so in the other. So it seems that unless you are a native speaker or learn specific cases where it is OK to drop them, the safe bet is to always include them.
"Would you slice the bread and cheese" is the correct grammar, not the commonly misused "Could you". I do not mind the common usage being accepted, but should not he correct usage be accepted? Would you is used for asking someone to do something, could and can are used if you are asking if someone is capable of something.
Something like the difference between можете and уметь possibly.
I strenuously disagree with your characterization of "could" as grammatically wrong. "Could you" and "would you" express different requests which have some commonality of purpose (slicing the bread). There are simply too many unknowns surrounding the request to determine the correct syntax in English, but можете means "to be able to do, to [can]", while "would" is more a conditional tense which gives the person asked the option of slicing or not slicing the bread. "Could" is only optional if the person is unable to perform the task for any reason, and more closely translates можете. Perhaps by now the moderators are accepting "would", but that's actually a 2nd best selection, not a 1st.
Well, можно means "may I" as in "is it permitted" or "is it allowed." The problem is that it is conjugated for the second person: можете. You would not say "May you slice the bread and the cheese," so I think the correct translation would be somewhere between "can you" and "would you." Either should work.