what indicators can be used to classify a group of stocks?
Question 1:
Geograhic location, market sector, it all depends on what you're trying to achieve with the clustering.
Question 2:
Yes. Adding too many indicators will cause your data to overfit and at some point you'll end up with every cluster having 1 member. I would use a regularisation penalty term to counter this. Either L1 (Lasso Regression) or L2 (Ridge regression) would work for this. Or you can use Elastic Net which would use a portion of both.