I understand why you think your pay rate would not be appropriate on the FMLA form. The hours you work might be relevant, though, to the medical issue at hand. I don't see the connection between the doctor certifying the FMLA form with the pay and hours described on it and how that might undermine the EEOC investigation on what I assume was a complaint of illegal discrimination based on disability.
As to the part about working from home, there are two distinct issues I see. First, the company cannot discriminate against you because of your disability. Thus, the company could not deny you the ability to work from home because of your disability. The fact that they let some other employees work from home raises the issue of what the reason is that the employer won't let you work from home. If the reason is something OTHER than your disability, that's legal for the employer to do. If the employer cannot give a good answer as to why you are not allowed to work from home when others are, that's troublesome for the employer. This part matters for a request to work from home that has nothing to do with accommodating a disability.
The other issue is, of course, if you are asking to work from home as an accommodation for a disability. An employer must provide a reasonable accommodation to assist a disabled employee to do his/her work unless that would impose an undue hardship on the employer. But note that the employer need not necessarily provide the exact accommodation that the employee requests. So, if the employer can address the problem in some way other than letting you work at home, it is allowed to do that. However, if the employer claims an undo hardship, that's going to be tough to pull off when it already allows others to work from home.