Not clear on that--they just "feel our pain"

First, about BOGO's, or anything that has a requirement that it be given at check in, yes, have two copies, but also, when you give them the first copy, have them go make a copy of it, and give you the copy back with a notation that it was received at such and such a time and date, and signed by the person receiving it (with their name and position printed underneath), and then when they do not have it at check out, and you give them the second BOGO you printed out (at home), and SHOW them the receipt you received from giving them the first BOGO you turned in at check in, they are embarrassed, and also much more polite and accommodating. I have done this with everything that I use as payment or as a coupon that must be given at check in. Also, when they lose it and you have proof, you can use this as a basis for a complaint to Customer Service or Mr. Marriott's Office of Consumer Affairs.

Yes, you absolutely are supposed to receive points AND room nights credit for BONUS BUCKS, PREMIUM POUNDS, SAVVY SAVINGS, MARRIOTT CHEQUES, or MARRIOTT GIFT CARDS. Applying any of these as a discount is WRONG! Many hotels apply these items incorrectly, and it is necessary to make some calls to get it straightened out. I have had to make several calls on different occasions for these problems.

Yes, absolutely correct, just as if you paid cash!

Hotels are reimbursed for BB, PP, SS, etc., although I do not know what the reimbursement rate is, and I am not sure that it matters to me what the reimbursement rate is either.

Yes, absolutely correct, it should be applied just like cash. I have had FDC have issues with how to apply BB and SS and Marriott Cheques to my folios, and often have to make calls to get that straightened out and to get proper rewards points and proper room nights credits.

It is less than 100%, however, I do not know the correct reimbursement percentage, or whether it is consistent across all of the brands.

BOGO certificates are a form of payment, and yes, Bonus Bucks, Premium Pounds, Savvy Savings, Marriott Cheques, Marriott Gift Cards should all be applied as payments, just as if you gave them CASH, and all qualify for MR points and room nights credits.

Has anyone got these to work at other Marriott Brands ?

Never tried, but it will not work.
The cert is very specific as far as what brands are covered, and also states certain properties of that brand are excluded.
Also when redeeming you are supposed to call Marriott Rewards to have it applied and they will not allow to do it either.