You've taken the biggest step to turning bowls, the first. If this experience doesn't discourage you you'll be hooked soon.
I've used some walnut grade lumber, and found that it isn't the best. I had a piece of 8/4. Walnut can be turned to a great finish, but when too dry i've found it to be hard to get that good finish.
Your tools need to be Sharp, not just pretty sharp, and kept that way, but more importantly a good finish comes from good technique - that means practice and patience.
You're describing a lathe that is sorely in need of repair! The bearings either need to be tightened up or replaced. Any movement is bad, that much sounds like one (or more) of the bearing-caps has come loose and may be lost in the dust of the floor. Get it fixed first, then you'll find your turnings will be getting lots better.
mike