1. a 35% pot sized c-bet is really small and looks really weak. However, we need to look at effective stack sizes.
you have 30BBs and to keep things simple, lets say blinds are 5/10 and your stack is 300.
-You make standard 4x BB raise with AK and get 2 callers. + Blinds, the pot is now 135
-Flop is A 2 8 rainbow and you c-bet 35% or 50 chips (rounded up), which isnt even half the pot. The pot is now 185
-Villain raises 155% the pot or 290 (rounded up). The pot is now: 475
-Your remaining stack is 210. You need to call 210 to win a pot of 475, getting 2.2:1 on your money.
Easy call with your strong hand (TP/TK) and after you've put in 1/3rd of your stack into pot already, you should be looking to get the rest of your money in. If you're against a set, then it's just unlucky and you're paying them off. Against 2 pair like A8, you're at 12% to win by the river and if they have A2, your'e at 24% to win by the river. However, you're in a good position to win if villain has a weaker A or a pair.
The more I think about it, the 35% pot sized bet is perfectly fine if you're looking to get your money all in and you want to look weak. You open the doors for the villain to play hands like 1010 or 89s aggressively to try and push you off. I think c-betting strong might be bad if villain doesn't have an A because it pushes them off the hand. With that stack, you should bet taking the best approach that gets all your money in.
2. Just because they're aggressive doesn't mean you need to risk your tournament life early on, but it would ultimately be up to you. It's still early in tournament and lets say you have a 100BB stack, you're not giving up a lot by raising 9BBs and folding to a shove. If UTG has any pair under AK, you're in a 50/50 situation and if they have any non-paired hand without A or K, like 10J or QJ, you're roughly a 60% favorite to win. So, to make a profitable call, the pot should be laying to to 2:1 or 1.6:1 respectively.
Lets say effect stacks are 1000 with 5/10 blinds.
-UTG raises to 30
-You 3bet to 90
-UTG shoves all in.
-Pot is now 90 + 30 + 15 + 970 = 1105
-It's costing you 910 to win a pot of 1105, only giving you 1.2:1 odds
. This is much less than the odds of your hand holding up, so it should be a fold. However, like I said, it's up to you if you think you should risk a possible 50/50 or 60/40 situation this early on in a tournament.
Best case scenario is if they have a hand like KQ, AQ, AJ where you're dominating and are an 80% favorite to win and the pot is just barely giving your the right odds to call (slightly under) but you can only really make that call if that's what you think they have. Again, it's risking 100BBs, so even in that situation, I still think a fold is the right play. Worst case is if they have AA or KK.
So, as played, I think it's an easy fold preflop this early in the tournament. You aren't getting the odds to call in what's most likely a 50/50 or 60/40 situation. I think the 3 bet preflop was fine with AK, though. You were just put into a tough situation early on. There is also the option of just calling against an aggressive player, hope to flop strong, and let the aggressive player pay you off.