a) By default in the Lightroom folder within My Pictures / Pictures
b) Always in the same folder as the catalogue
c) Wherever you tell it - which should be somewhere different. No backup of Previews.
Re 2, just move the catalogue in Explorer / Finder, double click it. If you didn't move the Previews, LR starts a new one in the same folder as the catalogue, following (b) above.
Re 3, answered above. Backups can / should be elsewhere and it's your choice where.
Notice that in Catalog Settings there's a Show button that reveals where your catalogue is.
My own personal clarification: Backups should be on a different physical disk. If you put backups on the same physical disk as the active catalog, and your hard disk crashes, you have no copies of your catalog. If you put the backup on a different physical disk and the hard disk with your active catalog fails, you still have one good copy.