$65 NLHE MTT: Defend BB vs min raise?, how can I fold

So I was playing a small buy-in live tournament. Field of 56, 5 itm. Blinds were 1500/3000 ante 500, I had stack of 53000, all stacks were pretty similar at my table. Only had a few hands at this table but most seemed to be playing pretty nitty at this point. So my BB I get 10 8o, guy min raises from MP, folds to me. Obv I am behind, but I don't think anyone is getting tricky with a big pair here, there is 15500 in pot now counting my BB (3000bb+1500sb+5000antes+6000 bet from mp) and I just need 3000 more to call. I know I'm probably 35-40% but just seemed I was getting too good odds to just lay it down without a fight. As you get close to that dreaded 10bb stack is it right to give up hands from bb even though pot odds are good? I felt like it was worth the shot, but after hand thought, "what kind of flop was I hoping for?, 10 high, 8 high?, what do I do than? shove and hope no A8 or A10?" Turns out I get worse flop I could (unless it ends up hitting), 7 9 K, rainbow. Now I felt stuck to hand and have to call his 8k cbet into the 18.5k pot, even though the K is in a lot of hands in his range here. For some reason he got scared (i guess) and checked down turn and river (10 and 3 respectively, no flush possible). Which leads to next question, do I shove either street hoping he somehow folds, I doubt he would of folded his AK, but now I was left with like 38K and pretty ss'd. I'm thinking maybe I should of shoved river, after he checked turn, make him worry about straight or 2pair.

I know I'm not suppose to post how hand played out completely in first post, but kinda had to put in to get to 2nd question, which is what I'm really looking for opinions on.

Without a reading on the player it's hard to say for sure what I would do. From what you say he is far from aggressive.

What hands would you possibly shove on the river? QJ and J8, of course. Maybe a set. Would you go all in with two pair out of position with possible straights on the table? I'm not sure. It really depends on the image he got from you in that hand and in the whole tournament.

His hand is somewhat predictable, he probably has a K. If he had two pair or better he would most likely bet the turn again. It all comes down to what you can make him think you have. Going all in from out of position is a show of strength, but I've seen people make some great hero calls with less than top pair.

Maybe after 10 on the turn you should have portrayed something like a straight and at the same time check the strength of the 1010 pair. After 3 on the river, your push will not look very convincing and many weak players who do not like a raise with a weak kicker call without thinking with Kx. Just above, the guy put his entire stack, calling all-in with a pair of jacks lying on the board.