Can ridge regression be used for feature selection?
Regularization of Ridge causes its weight to become very close to zero, but not zero. In contrast lasso can make weights equal to zero because of the types of regularization they use.

I would recommend to use lasso if you have lots of features, and you think just few of them are important. Otherwise, even though your model becomes simpler you will have a poor accuracy.

There is ElasticNet which combines both, but it is more expensive since it uses two regularization.

I didn't really understand what you ask by 


  Can the number of zeros in a weights vector change from zero to something else?


If you determined number of parameters beforehand their weights are unknown yet, not zero. That's what you are trying to find.

One last thing, for feature selection there are other methods. These(ridge, lasso) are just linear models for regression. If you want to identify which features work best etc. I suggest you to do a research on methods for this.