How to grant permission dynamically in android, i.e while running an application, Is this achievable?

I have few doubts.

1. Is it possible for Android application after installation, to ask user for permission for accessing certain functions? Like say the app A wants to read contacts for a specific purpose. If the user grants permission, then the activity will take place. Else it wont. Is it possible?

2. Is there a way of allowing user to select/de-select permissions during installation time?

3. I have read that using CyanogenMod grants user these kind of priveleges. Is there any solution for non-rooted user, apart from take-it-or-leave-it approach?

It would be great, but not, all permission must be granted during installation :-( Only exception is access to the google profile, this will be authorized during first access. I hope that a future android version will can do that.

Cyanogen can do opposite. You must grant all permissions during install, but you can explicitly remove them later. But it result in application crash very often. This is only for advanced users.