Rivets are usually pretty easy to replace, even if broken. Typically, you can drill out a solid rivet (just MAKE SURE NOT to enlarge the rivet hole...otherwise you can't put in a new rivet of the same size).
Most Airstream rivets are Olympic rivets which have a smooth head. This is done with the right rivet (check
https://www.vintagetrailersupply.com/category-s/205.htm). Get a ratcheting rivet gun with multiple rivet size pullers - go to a Lowes or Home Depot for a lower cost than any of the trailer specialty stores online though.
After an Olympic rivet is in you can use a specialty drill attachment (yes it costs more than the rivet gun or the drill...grrr. Here's the link -
https://www.vintagetrailersupply.com...-p/vts-177.htm) to smooth down the head and create a clean smooth appearance.
Re leaks in the trailer. Always check seals around skylights first. Then gaps in aluminum panels.
Remember "All Airstreams leak". Just minimize the problem. Do not put a cover onto an Airstream. It acts like sandpaper and will ruin the aluminum finish.
Best if stored under a car cover. Just make sure it can't distort in wind or collapse under snow.
Have fun!