With a switch on 3.0 you can pretty much run all the emulators made/ported for the switch, and there are a lot of emulators for a console with such a young scene, check out the switchbru site for the emulators.
As for backups, yes you can run backups, but most don't save, most don't even work, isn't easy to get them running as it requires a lot of trial and error, you can go the route of piracy only software with team excuter's SX OS, but I don't see a reason why you should go this route because backup loading will be free and easy soon, check out the ReiNX cfw which will be free and apparently include a backup loader.