ACROSS
1a 3d. Anagram ("Variously") of ACCEPTEDAS
4a. DIG reversal + D[irt]Y
6a. Cryptic def. (or conceivably double-def.) - ref. Blackbeard's ship, the Queen Anne's Revenge.
7a. Double def, and a nasty one ;) "State" is used as an adjective for national, in e.g. "state secrets"
DOWN
2d. POT (grass) surrounding IN (popular)
4d. Hidden word, madaGAScar
5d. Reversal of also=AND