If the VA raises your disability rating on an appeal, from 30% to 70%, do you get back pay from the date of your original claim?

Yes. The day your claim is accepted by the VA will be from this computational point to about six months duration. My first compensation check came this month, after my claim had been accepted in January 2018. No letter of explanation has been received at this point, but I imagine the VA will get around to it eventually. Good luck, friend!