Cannot delete or move apps, cannot use spotlight search

When I press and hold icons to get them into the "wiggle" state, they will wiggle briefly then return to normal - much much too quickly to be able to move them ror delete them. Additionally, when I try to use spotlight search, the search bar drops down then quickly disappears.

This happened after I resored my iPhone 4s from a back-up (my contacts spontaneously disappeared). I then upgraded to an iPhone 5s and put the 4s's restore one the 5s...

oh and it is chewing through battery life like crazy as well.

Can anyone tell me what is going on with my phone?

Thank you