The be-verb is optional in S. "S = NP" is completely valid grammatically. Also "adj = BUN* verb | B* NP be-verb" if you allow "i-adjectives" to be classed as verb phrases (as they were historically) and "na-adjectives" to be "noun-phrase ni aru". So you would actually get:
SENTENCE = VP | NP
VP = BUN* verb | BUN* NP be-verb
BUN = NP pp | adv
NP = VP? noun
I'm also not sure about the fact that "adv NP be-verb" is allowed by this grammar...Edit: spelling