My friend was rear ended (not at fault) when the cops showed up he found out his license was suspended. Will this affect the other insurance paying for the damages?

It should not, but it will mean he will get a ticket.

This should not effect the other insurance company paying for the damages to your friend's car. Your friend will probably get a ticket though.

It should have no bearing on them paying. They may of course use it to try and deny it at first, ( many insurance companies often deny claims at first)