Re: Adjectives or Adverbs
The rule is for when 'be' is a linking verb, not when it is an auxiliary verb. Here the main verb is 'shining'. In this particular case, you will see the adjective used by some speakers, though grammar purists would favour the adverb.
Re: Adjectives or Adverbs
Ho, dinilein,
The issue does have some pitfalls.
Of f course, nouns are defined by adjectives and verbs by adverbs, but there are quite a few cases when adverbs have the same form as adjectives: late, close, right, straight etc.
Besides adverbs are shortened in some collocations or informal speech:
hold me tight
go slow
real nice
I am not sure your 1st sentence is OK. Bright may still refer to the noun -moon.
Regards