Is making a rabbet joint on the end of a bumper against the rules (rule 21 a specifically)? This would mean that part of our bumper is approximately 3/16in thick instead of the required 3/4in thickness, but our other bumper that is connected to the joint will give it the 3/4in thickness. Here is an example of what it would look like: http://www.woodworkersjournal.com/wp-content/uploads/1-Simple-Rabbet.jpg
I think it’s important to note that the plywood does not have to enter the corners at all (R21B, bottom right image). I would say that the joint is OK.
For the metal segment, that’s a “no”–there’s nothing in the bumper rules allowing it (and bumper rules are the one part of the manual where if it isn’t in the rules, it isn’t legal). HOWEVER, if you were to design that as part of your attachment system, that would be fine, I think–but it would count against bumper weight.
It is not one of the corner configurations shown in the game manual, and as Eric noted, bumpers are one of the few cases where something is not allowed unless it is explicitly allowed. As such, I would suggest a Q&A if you are considering this. The half-thick pool noodle on the rabbet side will not have the usual compression characteristics of pool noodle, especially if cored. Corners are where you want the bumpers to work best.
Note that the wooden part of the butt end may not extend more than 1" beyond the frame perimeter ber R21 b. When/if you submit your question to Q&A, I would also include in the diagram where the wood is located.
I would not consider rabbeting the wooden part of the joint to be legal, per R21a, as that part of the wood would only be (e.g.) 3/8" thick.
