Can I move a folder into another folder?

Yes.  Again, by first left swiping on the folder name, you expose the folder level actions you can perform.  Then tap 'More...'

This will show the rest of the folder level actions where you can tap on 'Move'.

 

 

You can then select the folder you wish to move to by tapping on the destination folder name and 'Choose', or you may create a new destination folder by tapping on 'Create' and entering the new folder name.