Baselinker

What happens if we remove a product from the catalog in Baselinker but leave it in Ergonode?

The product will not add itself again when you synchronize again.

What will happen if I change category name and sync it with Baselinker?

You Ergonode category name cannot be changed, you may only change Translation name of it. So if you change translation name of category it will change in baselinker as well. New category will not be created.