Is it possible to simply answer 'आ' if someone is asking me how long he/she will have to wait (just in order to give a very quick response like in English)?
Simply saying "आ" would be like saying "Come!", as in you are asking the other person to come. (Note: It is in the first level of formality. More formal forms are आओ and आइये).
"Coming!" would be "आ रही हूँ" (i.e, omit the मैं).
No because Hindi is not like east Asian languages
It needs to be said in full or almost in full
Hindustani people often speak very fast anyway so it doesn't matter
I gave yall 3 lingots