It will not come with an ATF approval letter. Those letters can be found under the Resources section of SB Tacticals website.
I believe the picture you are asking/referencing about has the Surefire flashlight forend installed on the Mossberg.
It is a fixed position stock. There is no other position for it.
No this kit will not work for the Remington tac 14 but this will https://www.opticsplanet.com/sb-tactical-stabilizing-brace-kit-for-remington-tac-14-sbm.html
No this will not. But if you use this one https://www.opticsplanet.com/sb-tactical-buffer-tube-folding-adapter-2-position.html it will work then.
Here is a Forward sling mounting for Mossberg 590 https://www.opticsplanet.com/magpul-industries-sga-fwrd-sling-mnt-moss-500.html
Yes this will work for your 590m shockwave as long as its a 12 GA and or 20 GA
No this will not work for Rock Island VR80 since the stock is not removable.
No this kit will only fit 12 and 20 GA.
As long as the Mossberg 590 Tactical is 12 or 20 GA it will work