Bumper bracket spacing?
We see that the bumpers need to be supported by the frame every 8 inches. We have a solid frame around our robot. Do we have to have brackets every 8 inches?
How far from the corners?
As far as I know there are no rules dictating how many brackets can be or are required to be on the bumpers, I would recommend at least four and would push to have more then that if room allows. Since you have a solid frame you don’t have to worry about the bumper being supported every 8 inches that is a requirement of having gaps in the frame. As for bracket placement that is entirely your teams discretion, place them in spots that you can access easily with your hands so you can swap bumpers quickly if you have a short turnaround between matches.
Our team uses two clips on the front and two on the back, as well as 3 more redundant slot in bolts on either side that are not neccesary.
If you have something like a Kit-Bot, you only need enough latch/attachment points to effectivly hold the bumpers on. The bumper rules in the game manual only say “bumpers shouldn’t move.” The bumpers should attach to the robot, with enough mount points to stay attached during competition match play.
This means the bumpers have to be backed by contact with the frame every 8 inches - not that they have to be attached to the frame every 8 inches. The intent is to avoid having large spans of bumper wood that are unsupported, as a hit in such an area is likely to split the wood/cause bumper failure.
As others in this thread have said, you need enough attachment points to keep the bumpers securely in place. This doesn’t necessarily mean brackets + bolts (though that is one solution) - for example, you can have pins on the bumper fit into holes in the frame as part of your support, or bumper mounts that slide into C-channels attached to the frame, or other such things.
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This is a pic of our practice west coast drive we made last year. See the angle brackets i circled, we had to put thise on to keep support of the bumpers closer that 8". With the kit bot chassis there is no need to do something like this.
must attach to the FRAME PERIMETER of the ROBOT with a rigid fastening system to form a tight, robust connection to the main structure/frame
As many attachment points to do this. So a RI should not require a specific number. Only that the attachment be rigid. Also not a specific requirement, but good practice is that you should be a able to pick up your robot by the bumpers.
Although just to note, it’s generally a bad idea to lift your robot by the bumpers.
See Fig 9-9 in the Robot rules for a visual on the 8" unsupported rule.
It depends how well they are attached. 
Regardless how you lift your robot it is a good rule of thumb. NOT actually required by rule. We design in lifting points on our robots. Two people lifting a 150 lb robot requires care and consideration. Subject of a different thread.
I agree it seems like a good way to test that your bumpers are sufficiently attached. I was just trying to clarify that it’s generally better to be holding onto the frame directly rather than the bumpers. I’d expect that it’s possible to hold by the bumpers on many robots, but it places unnecessary stress on the mounting system. I also figured you already know it’s not advisable in most cases, but I didn’t want to leave it unsaid and have someone break their bumpers/robot.
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