TDIU, SMC-S, and back pay

My disability claim is currently in progress, currently waiting for the last set of DBQs to be uploaded. Hoping for this week.

I was fired in 2022 due to my PTSD. I'm unemployed today.

I've provided a work letter mentioning this. My exwife divorced a year later. She wrote a buddy statement. I have a nexus for severe PTSD from a Clinical Psychologist with a PhD and 38 years of licensed clinical experience. Finally, I have a PTSD diagnosis from a Navy PA while I was active duty.

I have read that TDIU backpays to the day after your last day of employement. I have 2 questions:

1. Is it true that TDIU back pays to a day after the last date of employment?
2. If I'm awarded SMC-S, how would this come into the picture if I'm also awarded TDIU? I'd guess I'd be entitled at the higher SMC-S rate, and my profile would also be marked as TDIU?

Thank you