I have simplified the question below and removed quite a bit of the information provided, as it is not required to understand the question. 

I want to apply for a mortgage. I am in my early 30's and work, but I am disabled and claiming [redacted], which provides me with [redacted] each month.  I question whether that money can be used to prove I can afford a mortgage.  

Lenders should accept the benefits you receive as part of your income.  There are two key elements to the benefit you receive.

1. The benefit you receive due to your significant disability will continue to be paid for the rest of your life.
2. The benefit is not means tested, so your income or savings don't affect it.

Based on the above, the lender can be confident that the benefit will continue to be paid for the mortgage term, so they have no reason to exclude it.  You may have to provide additional evidence to prove that it's a benefit that will not end.

Readers need to appreciate I am not revealing too much information about the person asking the question.  Her position requires lifetime support.  Not all benefits, even those not means-tested, will always last a lifetime.  

Mortgage lenders cannot discriminate because part of your income comes from benefits.  If you are applying for a 25-year mortgage term, the lender must be sure the benefit will last that long.  If this cannot be shown, they could exclude it.

As always, each lender will have their own policy for accepting benefits, so don't assume they are all the same other than they must consider them.