Think I got it all.

Villain's raise range is 166 hands. That's 78 for the pocket pairs, 40 for the suited stuff, 48 for the offsuit stuff.

Our hand is blocking some of those combos though. He's losing 3 ways to get 99, 3 ways to get AA, 1 ways from each of 4 A containing suited hands (total of 4), and 4 ways from each of the A containing offsuit hands (total of 9). Total blocked hands is 19, so really what we're looking at is 166-19 = 147 hands that he will raise with.

Villain will continue against a 3-bet with 27 hands worth of pp, 6 hands worth of suited, 9 hands worth of offsuited, total of 42. 42/147 = 28.57% continue, so 71.43% folds.

Now I'm gonna wave my hands. Over in the blockers howto thread there is an example that has the exact same betting sequence as in this quiz, and you said that we need him to fold 68.6% of the time. I don't (yet) know how you came up with that, but there it is.

71.43>68.6, so in answer to Q1, yes, it is profitable to 3-bet bluff to 12bb.

Q1. yes


Question 2:
Flop comes down Q94 rainbow, we want to know how often he hits top pair or better with the range in Q1. I hope I'm reading that right.

Of the hands that he called our 3-bet with, the following hands will give top pair or better: QQ, KK, AA, AQs. That's 3+6+3+3 = 15 hands, out of the 42 he would have seen the flop with, so 15/42 = 35.7%

Q2. 35.7%


Question 3:
To maximize our fold equity, we want hands that block as much as possible out of Villain's 3-bet-call range.

So let's see. Unblocked, he's got:

TT - 6 ways
JJ - 6 ways
QQ - 6 ways
KK - 6 ways
AA - 6 ways
AQs - 4 ways
AKs - 4 ways
AK - 12 ways

We want hands that knock out as much of that as possible.
5 TT - knocks out 5 ways
5 JJ - same as JJ
7 QQ - knocks out 5 ways from the PP and 2 ways from AQs, total of 7
13 KK - 5 ways from the PP, 2 ways from AKs, 6 ways from AK, total of 13
20 AA - 5 ways from PP, 2 ways from AQs, 2 ways from AKs, 6 ways from AK, total of 20

6 JT - 3 ways from TT, 3 ways from JJ, 6 total (hey!)
7 QT - 3 ways from TT, 3 ways from QQ, 1 way from AQs, total of 7
10 KT - 3 ways from TT, 3 ways from KK, 1 way from AKs, 3 ways from AK, total of 10

11 AT - 3 ways from TT, 3 ways from AA, 1 way from AQs, 1 way from AKs, 3 ways from AK, total of 11 ways
11 AJ - same as AT

10 KT - 3 ways from TT, 3 ways from KK, 1 way from AKs, 3 ways from AK, total of 10 ways
10 KJ - same as KT

11 KQ - 3 ways from KK, 3 ways from QQ, 1 way from AQs, 1 way from AKs, 3 ways from AK, total of 11 ways

14 AK - 3 ways from AA, 3 ways from KK, 2 ways from AKs, 6 ways from AK, total of 14 ways
12 AQ - 3 ways from AA, 3 ways from QQ, 2 ways from AQs, 1 way from AKs, 3 ways from AK, total of 12 ways

So our possible hands, sorted by fold equity at this point in the hand:

AA
AK
KK
AQ
AJ AT KQ
KJ KT....dunno why I did KT twice, but it's heartening that I got the same answer twice
QJ QT QQ
JT
TT JJ
everything else