Is there any application to ask question on stackexchange as well, instead of just monitoring a user timeline to get notifications?
Not a direct answer, but there is an effort underway to improve the mobile versions of the Stack Exchange sites.
I have used my Android browser to interact with the Stack Exchange sites and it works pretty well.
There is "DroidStack" which allows to Browse the Questions, Users, Tags and Monitor for Statuschanges, but it does not allow you to question yourself or write an answer. But you can open the current question, user, whatever in your favorite browser anytime. This comes closest to writing.
There are other tools, with similar restrictions, but I think DroidStack is the best of the ones I tested so far.
The problem is, that writing to any SE-site is (currently) not allowed via API, only via webinterface. Writesupport is planned for API-version 3.0, and will be bound to other reputationlevels then via web as stated in "Announcing API version 1.1" on StackApps.com?
Stack Exchange app is there in google play. You can ask question using this app.