Dan,
Time to get to know your local hardware sources. A good replacement for
belly rivets is an all aluminum 3/16 diameter shank, 1" long with extra
large head (about the size of a dime). If you can't find the extra large
head use aluminum washers on smaller head 3/16 rivets.
Yes there should be a down pipe from the fresh water tank. Find the tank,
find the drain and put a new 1/2" vinyl line 8-12" down through the hole
and fish it out so that it hangs underneath.
Charlie