Translation:Is there anything else you want me to do?
Haga is the correct form for yo, él, ella, and usted. We can eliminate "Is there anything else that you want to do" because for usted that would be "¿Hay algo más que quiere hacer?" So, that leave these three:
Is there anything else you want me to do? (yo haga)
Is there anything else you want him to do? (él haga)
Is there anything else you want her to do? (ella haga)
Any could be correct depending on the context. However, the first one seems the most likely under most circumstances.
No. Because the way the sentence is set up the subject of the first part of the sentence (quieres) cannot be the same subject of the second part (haga) or else it's not subjunctive and then you wouldn't be able to use haga. You can tell it's not usted anyway because "quieres" is in the tú form not usted. If you wanted to say "Is there anything more you want to do?" You would say "Hay algo más que quieres hacer?" You would just use the infinitive. :)
No. In this sentence, the only reason we don't know if it's me or him/her is because we don't have the subject of "haga" or the context of the sentence. If we could see the people talking and using this sentence or saw this sentence in a book, then it would be very clear who the subject of "haga" is. You also couldn't translate it as "is there anything else you want done?" because then it wouldn't be subjunctive anymore.
I didn't put "me" in my answer and still thought that my answer was right. Previously I had googled 'subjunctive' to try to understand the concept. (That didn't work too well I guess). Reading these comments has out-done my google research! It's beginning to sink in, thank you :-}
No because you are using the indicative and this sentence requires the subjunctive. You use the subjunctive for many different situations and one of them is for desiring/wishing. "Is there anything else you want me to do?" The person is wanting you to do something so it needs to be subjunctive.