"Θα απαντήσω σύντομα."

[strander91]

is "i will reply shortly" a possible answer?

[troll1995]

Yes. Added

[Lyazko]

Not "briefly" though, right? Since "briefly" would mean "in few words", but "shortly" means "within a short time"?

[optisamit]

And how to say "i will be answering?"

[D_..]

As far as I know, "I will be answering" can have one of two meanings in English: (1) that you intend to (provide one) answer in the future and (2) that you will be providing answer after answer after answer. For (1) it would be the same, for (2) it would be "θα απαντάω" (or απαντώ), which is the future continuous.