android ContextCompat.checkSelfPermission() not found

checkSelfPermission() didn't get introduced into the native Context until API 23. So you will need to use at least version 23.0.0 of the support library.

You should change this

compile 'com.android.support:appcompat-v7:22.1.1'

to this

compile 'com.android.support:appcompat-v7:23.0.1'

If you have migrated from eclipse adding the below line wont work

compile 'com.android.support:appcompat-v7:23.0.1'

While migrating, it adds appcompatv4 as an external dependent library. Make sure you have deleted the appcompatv4 library from the libs folder and then it should start working