I see two problems, both related to using newfangled Shimano stuff on a basic 8-speed drivetrain. If your Tiagra fd is 4700 series, that's a narrow 10-speed mech..you need 8-speed like Claris, or any old 7/8-speed derailer you can find on eBay.

I presume by your description that the cage on the rear derailer is actually rubbing the tire, not scraping spokes. This may be related to the Shadow design which tucks the rear derailer further back on mountain bikes to avoid catching debris. You should be able to fix this with a non-Shadow mech.

I love bar-end shifters..keep 'em if you like 'em.