Is it possible to have Skype for Android automatically answer calls?
Currently and sadly, there's no such option to allow the action of auto-answer an incoming Skype call.

You can keep an eye out on this threads, maybe in a nearby feature such solution will arrive:


Skype Support Network: Auto answer incoming call on Android OS
XDA Developers forum thread: [RQ] Skype auto answer
XDA Developers forum thread: [Q] Skype Auto Answer


Additionally, 3rd party solutions aren't possible to this end, since Skype uses a proprietary protocol with no available API as explained on this Stackoverflow answer.