have you checked for loose bracings or screws? That, and look for anything that might be stuck in the horn.
As for the first valve, I would recommend taking it to your local repairman. It may be a small dent in the casing, bad valve guide, bent valve stem, or something else, but mr. repairperson will be able to address it.
Plus if you haven't given it a chem clean in a long time, both can be done at the same time for a moderately lower price.
I dont know how powerful your tuba is but you say if you hold the bell it stops.....................maybe the solder disconnected off the leadpipe? Just a guess. I would have to know what kind of ring it was, otherwise i could also just simply guess loose valve caps :S Good luck
Lots of tubas have bells that ring; it can be very annoying. One way to stop it is with your hand. You can also wrap a towel around it. Or go to your local hardware store and buy some clear plastic tubing, slit it down one side, and slip it over the bell ring. That works for me. It's amusing that half of the tubists in this world are trying to encourage or enhance those vibrations by using awkward tuba stands and by separating the leadpipe from the bell, while the other half of us are trying to stop those same annoying sympathetic vibrations..
I have a band director friend who freelances, and has the "bell protector" on his M-W 11 and he says it eliminates the bell ring. On my old souzy, I wasn't so lucky. the bell was so thin, to save weight, that I had to go completely around the rim with golfer's tape to damp the non-harmonic ring. That's why Miraphone and others put that nickel "garland" around the bell.
Speaking of piccolos: do you know the real difference between the wooden ones and the silver ones? You can burn the wooden ones!