Is special permission required to take off from a field within restricted airspace?
The most obvious point to make here is that KMRH is not in restricted airspace: the sectional shows that it's in uncontrolled class G airspace, with class E at 700' AGL. But having said that, there is indeed a lot of special use airspace nearby:


W-122 is a warning area
R5306A and R-5306D are restricted areas
A-530 is an alert area


You can't enter the restricted areas without permission from the controlling authority, but you can enter the warning and alert areas if you want. More details of each area are on the sectional chart, the FAA's SUA site and JO 7400.8X.

Looking at the sectional, it looks to me like A-530 is a 'gap' in the restricted areas to give access to KMRH and the three private airfields nearby. R-5306 A and D are from the ground to 18,000 MSL (up to but not including FL180, to be precise) and operate continuously. If the A-530 airspace were the same then there would be no way in or out of KMRH (over land, at least) without getting permission every time. Because A-530 is sandwiched between two restricted areas, I guess there's probably a lot of military traffic around and that's why it's an alert area rather than normal class E airspace.