Question Title: finger numbs

From the spine are sent out "roots" which combine to form various nerve of the arm. So although a muscle is
generally suppplied by one single nerve of the arm, that muscle will often be supplied by several spinal roots. You
seem interested in the nerves themselves and what they do so I'll tell you about them.
I'll give you the main functions or most well known muscles of the arm - there are other muscles not mentioned but
I'm not sure if you want that detail.

Axillary Nerve - Supplies the Deltoid
Musculocutaneous Nerve - Supplies the Biceps and thus serves forearm flexion

The hand itself is supplied by three nerves:
Radial Nerve - which supplies the triceps and extensors of the wrist as well handles thumb and finger extension
Ulnar Nerve - supplies flexors of the ring and little finger and sensation on that side of palm and those fingers
Median Nerve - supplies pronators of the arm and helps in wrist flexion (along with the ulnar) but involves flexors of
thumb anf first two fingers and sensation on that side of the palm / fingers

This is a simplistic version granted and there are some complexities (for example, the thumb's actions are mediated by
the median,radial and ulnar), but it helps provide a rough guide.