I think the weird sound you are experiencing is a ‘wolf tone’. The following video gives an example of the sound, which with a little experimentation, you will find happens on one note on your violin. Depending upon who you ask, you’ll get different suggestions about how to solve the problem of a wolf tone on your instrument. In general, it is a permanent flaw. If you are playing this instrument professionally, you’ll probably want to make plans to replace it. The end of this video (if your ears can tolerate listening to the end) has a list of suggested solutions for fixing a wolf tone. Before you spend a lot of money on solutions that might not work, I suggest showing the instrument to a luthier and get a pro opinion on whether it can be remedied and whether the cost of fixing it would be more expensive than the value of the violin itself.
As to the bouncing bow, this is more difficult to assess. Even knowing the bow is literally made to bounce, it seems unusual that it would spontaneously begin bouncing from the tip, during an up bow. Generally, assuming it’s not something with the bow itself, I would suggest really experimenting with this problem too. See if you can isolate when it happens. At a certain point in the music? A particular bow speed? is there something happening in the bow arm (weight, speed) when you begin the bow stroke that initiates the bounce? Do you see the bow bouncing or do you hear it bouncing? Does it happen on all strings?
You mentioned the bow was not stored properly for several years. Is the bow begin over tightened now to make up for the loose bow hair? Does the bow maintain a curve (inward, toward the bow hair) when the bow hair is tightened? Try bowing with the first finger lifted off the stick. Does the bouncing still happen?
Here’s the wolf tone video: