There are 3 rivets holding that rail, two rivets would be enough.
It takes a lot of force to get the rivet as flat as you show in the pic so it's probably plenty tight in the hole as is.
So if the other 2 rivets look good, you should be GTG.
If that was a front trunnion rivet, I might think different.
The rest of the rivets in pics look great.
no, rivets are set when cold but you need a dimpled plate so you don't flatten the head.