Store Apps -- Mail is one -- should update automatically.

If they don't seem to be, click the Store icon in the taskbar. When it opens, click the little icon immediately to the left of the search...

Whatever you do, you can't upgrade from 8.0 to 10. You need to be on an activated 8.1. If you do that upgrade as Microsoft wants you to do, the 8.1 activation will transfer automatically to that 10...

The Mail app in W10 does not enable folder renaming, creation, or deletion.

If you are using an outlook.com account, or something similar from Microsoft, you should be able to edit folders via...

You can upgrade from 8.1 or buy an install image for a clean install. The 8.1 activation will be transferred to W10. You'll get a key when you buy an ISO online.

Explore the reset/refresh options...