Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Is it permissible to listen to chants praising the Prophet if accompanied by musical instruments?
If singing, or chanting in praise of the Prophet was accompanied by a forbidden musical instrument, then it is forbidden.
Is it permissible for a girl to wear colored contact lenses?
All Perfect Praise is due to Allah, The Lord of The Worlds.
Wearing colored contact lenses for medical treatment is permissible, and wearing them as an adornment is also permissible, provided that she isn`t seen while having them on by non-Mahrams. And Alalh Knows Best.
Does an internal examination require ghusl?
Ghusl isn't required for making internal examination; however, it invalidates one's fasting. And Allah Knows Best.