If I have added extra fields to a user profile, how can I programmatically check if those fields are empty?
I would advise against keeping those fields around after an uninstall. It's a module's responsibility to clean up after itself, and a user of your module should be able to assume that if they disable the module, the functionality will be gone, but the data remains in the database.  If the user uninstalls the module, the assumption is that the module will clean up after itself - delete all its data, custom tables, created variables, etc.

If you don't want to lose any data, just disable your module without uninstalling it - then the uninstall hook doesn't run.  But my suggestion is to keep to the community's expectations and properly clean up the custom database tables, fields and variables that your module has created in the uninstall_hook.

I think with open source projects like Drupal, where there are tons and tons of contributing authors and contrib modules, it's even more important for each of us to conform to the expectations of a module's behavior.  Otherwise, if each module does what it wants upon uninstall, we wouldn't know what to expect in terms of our databases.  What if a user has another contrib module that conflicts with your module's fields, for example?  How could they ever get rid of them if your uninstall hook doesn't clean them up?