I misread the original post so I'm using $12.25 and not $12.35.

1) We must call $6 to win $12.25 or 2.04:1
2) >= 33%
3) 56 combinations ( 4x6 combinations of pairs, As, Ks, Qs, Js, 2x16 combinations of suited and unsuited non-paired cards AK and AQ)
4) 24/56 are overpairs, top set is not in his range. If 24 combinations are overpairs 32/56 combinations are unpaired hole cards. 42% of his range is overpairs.
5) There are 44 combinations of hands in his range. 6 combinations of JJ, 6 combinations of QQ, 16 combinations each of AK and AQ.
6) 12/44 are overpairs, top set is not in his range. if 12 combinations are overpairs 32 combinations are unpaired overs. 27.2% of his range is overpairs.
7) 15 outs, 9 diamonds, any 9, and any 4 (not diamonds).
8) 21 outs, 9 diamonds, any 9, any 4, any 8, and any 6
9) 12 outs, any 8, and any 6, any 4 or 9 that's not a diamond.
10) There are 15 combinations of AK or AQ that are not specifically the Ad{K,Q}d, 30/44 a bit more that 68.2% of his range.
11) There are 2 combinations of AdKd and AdQd, 1 each. This comprises 2/44 or just under 5% of his range.
12) (15/46)(12/24)(12.25) + (14/46)(12/24)(12.25) + (31/46)(12/24)(-6) + (32/46)(12/24)(-6) = -.2473
13) (20/46)(12/24)(12.25) + (19/46)(12/24)(12.25) + (26/46)(12/24)(-6) + (27/46)(12/24)(-6) = 1.7364
14) (12/46)(12.25) + (34/46)(-6) = -1.2391
15) This is complicated, because sometimes he's counterfeiting your outs. 3 combinations of each pair contain a counterfeiter.
But AK and AQ are also in his range so 12 more combinations are counterfeiting your outs. So 24/56 combinations counterfeit
a single flush out. The expected value calculation would be:
(15/46)(24/56)(12/24)(12.25) + (14/46)(24/56)(12/24) + (21/46)(30/56)(18/30)(12.25) + (20/46)(30/56)(12/30)(12.25) + (12/46)(2/56)(12.25) +
(31/46)(24/56)(12/24)(-6) + (32/46)(24/56)(12/24)(-6) + (25/46)(30/56)(18/30)(-6) + (26/46)(30/56)(12/30)(-6) + (34/46)(2/56)(-6) = $0.2901 +EV
16) (15/46)(12/24)(12.25) + (14/46)(12/24)(12.25) + (31/46)(12/24)(-6) + (32/46)(12/24)(-6) = $0.2473 -EV
17) 12 combinations. (15/46)(6/12)(12.25) + (14/46)(6/12)(12.25) + (31/46)(6/12)(-6) + (32/46)(6/12)(-6) = $0.2473 -EV
18a) (15/46)(12/44)(6/12)(12.25) + (14/46)(12/44)(6/12) + (20/46)(30/44)(18/30)(12.25) + (19/46)(30/44)(12/30)(12.25) + (12/46)(2/44)(12.25) +
(31/46)(12/44)(6/12)(-6) + (32/46)(12/44)(6/12)(-6) + (26/46)(30/44)(18/30)(-6) + (27/46)(30/44)(12/30)(-6) + (34/46)(2/44)(-6) = $0.6202 +EV
18b) (15/46)(12/14)(6/12)(12.25) + (14/46)(12/14)(6/12)(12.25) + (12/46)(2/14)(12.25) + (31/46)(12/14)(6/12)(-6) + (32/46)(12/14)(6/12)(-6) + (34/46)(2/14)(-6) = $0.3890 -EV
19) You have to call $2 to win 10.25 or 5 1/8 : 1 or about 5:1 you need a little under 20% equity.
20) You have to call $2 to win a minimum of $4.35. Direct odds are 4.25:2 or 2 1/8 : 1 you have to have at least 30% equity or more.
If villain will either go all-in or fold to any bet, and his hand is in the non-stackoff range our odds are 2.125:1 we need 32% equity.
21a) 24 of 56 combinations are pairs 12 of them have one of our outs counterfeited (12/56)(9) * (12/56)(8) * (18/56)(15) * (12/56)(14) * (2/56)(6) = ~10.2 outs for the range
21b) Same as A. his range on the flop is the same for A and B, 10.2 outs for the range.
21c) 12 of 44 combinations are pairs, 6 counterfeit a flush out, (6/44)(9) * (6/44)(8) * (18/44)(15) * (12/44)(14) * (2/44)(6) = 8.6 outs for the range
21d) Same as C. his range on the flop is the same for C and D, 8.6 outs for the range
22a) (10/47)+(10/46) 43% equity against villains range, it's an easy call, as we only need 20% equity.
22b) He shoves 26/56 or 46.52% and folds 53.48%. (26/56)((10/47)+(10/46)) + (30/56) = 73.54% equity, easy call because of fold equity.
22c) (8.5/47)+(8.5/46) 36.56% equity against villain's range, again easy call as we only need 20%
22d) 14 out of 44 combinations shove 30 out of 44 fold. (14/44)(.3656) + (30/40) = 86.63% equity against villain's range.
22x) I believe we can profitably call in all scenarios A,B,C, and D.
23a) $7.74 assuming we have 43% equity on the flop.
23b) If we have 73.5% equity (due to fold equity) in this scenario, villain can not bet enough to take away our implied odds (and avoid becoming pot committed in such a way as to violate the contraints of scenario B)
23c) $5.89 assuming we have 36.56% equity.
24d) Same as B, villain can't bet enough without pot committing himself in a manner that violates the exercise.