Is it permissible for one to shake hands with his uncle`s daughter?
No, it isn`t because he is a non-Mahram (Marriageable) to her.
What is the ruling on one who slept while firmly seated on the ground, regarding nullification of ablution?
The default ruling regarding sleep is that it nullifies ablution. An exception to this is one who slept while firmly seated on the ground; his ablution is not nullified by sleep if he wakes up while still firmly seated on the ground. And Allah the Almighty knows best.
What is the expiation for perjury?
Perjury is forbidden and one of the major sins that require turning to Allah in repentance, seeking His forgiveness, giving back rights to whom they belong, or seeking their forgiveness, and expiating for that oath.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.