Position of Adverbs in Negative Sentences [closed]

All are grammatical (though A2 is a bit odd), and the 1) and 3) forms are synonymous. The 2) forms mean something different, along the lines of "it is not certain that" and "it is not obvious that".

In both examples you give, 1 and 3 are correct. The important point being that the adverbs certainly/obviously have to stand before the negative.

By placing the negative before the adverb in case 2, you change the meaning of the sentence. A2 raises the possibility that Lila could 'be very happy about it' but not certainly so; whilst A1 and A3 makes it absolutely clear that Lila definitely will not be happy about it.

In B2 you could be 'paying attention to the signs', but not obviously so. In B1 and B3 you are clearly not paying attention to the signs.