Adjective for something that can be responded to

It felt wrong because -able forms adjectives from transitive verbs — doable, drivable, killable, reversable, callable, wearable. But respond is not a transitive verb. Find a transitive synonym, and then slap the -able onto it. For example, answerable, fieldable, addressable, handleable, acknowledgeable.

The nearest you’re likely to get is answerable, in the sense ‘Capable of answering requirements, purposes’ (Oxford English Dictionary).

Based on your update, you might consider:

feasible: possible to do easily or conveniently

workable: capable of producing the desired effect or result; practicable; feasible

Other options might include viable, achievable, or attainable.

_{(Definitions from NOAD)}