>Will the MC-30 remote shutter release fit in the D800 port?
Yes, it will; the D800 has a standard 10-pin socket
>Also, will the EH-5a power supply work with the D800?
I don't know what the differences are between the earlier EH-5a and the EH-5b that is listed for the D800. The EN-EL15 battery which powers the D800 differs in both charge and voltage from the EN-EL3e which powered the cameras that used the EH-5a, I'm guessing that the two units are not interchangeable.
I expect you are correct, but it's dangerous to just go by what Nikon websites say - they maintained only the EH-5a, and not the earlier EH-5, was compatible with the D700, whereas in fact either of them works fine