the piece you guys are talking about is called the rear cross-member which has 2 body mounts on it. i cannot speak for all bumpers ever made but the overwhelming majority of bumpers will bolt to the cross-member.
as for how the fuel tank is mounted is via the skidplate. the tank is strapped into the skid-plate, and then the skid mounts to the rear cross-member, and the next cross-member forward. on the two frames i had, my 85 frame had the "studs" which are actually just small carriage bolts with keeper. the other frame i had was earlier, i forget what year, but had the short shock towers. that one did not have any bolts or anything, but i suspect that was a replacement cross-member.