Pretty standard I suppose. I also think you might get called pretty lightly given the draw heavy nature of board.

I would check fold the turn.  To be honest, thats not even a great board to C bet IMO.  The board is very wet, and also its very unclear as to what outs will be 'clean' for you. There is plenty of 7X, 8X, 9X, and TX in the average players 3 bet calling range pre flop, as well as suited stuff.   Whats your plan if he raises the C bet on the flop? You can't really call, then check fold turn.. There are going to be far too many turns that you will be check folding.  Anything 2-J is going to be tough to play.  Any diamond is going to be tough to play. Once he calls your flop C bet, you are often behind.  The 4 changes nothing on the turn, so he is likely to call another bet.  By check shoving you are giving him 31%ish pot equity to call.  Against your hand, his range is going to have better equity than 31% (although its likely he isn't caring about that). So the question is, can he fold enough?  I think the half pot bet most of the time on the turn is the sign of a hand that is going to call a shove *most* of the time, and fold *a small %* of the time.  I think if called, you are rarely ahead, so they MUST fold a HUGE % of the time in order for this to be profitable. FWIW, I think check folding > check-shoving > C betting turn.

Actually, calling the turn is profitable if i calculated correctly. You need 25% equity and u have 31% if we give villain fairly wide range.  I'd shove any Q and 9 rivers, even diamonds, because only 4 diamond combos beat you in both cases. Also, I would check/call river if J comes and I know that villain is capable of bluffing in that spot. Because if he is he has 90 combos that we can beat in his bluffing range, and 70 value combos.

I'm not sure I understand what you're saying. Are you saying that check calling the turn is profitable?  Do you still think check shoving is the best line, or are you saying that check calling is the best line?   I dont think you can give your opponent that wide of a range given he has called a 3 bet pre flop, and then a c bet on the flop.  He's unlikely to have complete air by this point.   The turn bet villain makes is offering you 25% pot equity.  Even if all 9's, J's and Q's give you the best hand thats still only 10 outs, giving you around 20% equity. Thats not taking into consideration that any diamond out might be bad for you, and any J might be bad for you.   Given that you need 25% equity in the hand to make calling the turn bet a break even play, I don't see how it can be profitable to call.  Im interested to know what range you have given your opponent to calculate hero having 31% equity on the turn with one card to come.   

You're right, I ran the numbers again in pokerstove, and now im getting 20%. I guess i did something wrong last time.Tbh, the more I think of it, the key to decision is that its a 3bet pot, otherwise any aggressive line on this board would be much more profitable.

in the first of all I recomend flat calling qj pre at this stack depth or if you know you opponent calls wide is good to 3bet but most cases i think flatting is the best .on the flop i really dont see a cbet here there so many draws and combos that could call a cbet and will make the hand of your villian very hard to read , i think best is a cec / call and fold to a bigger bet on the turn from 1/2 pot or more in the line you took i think  i would cec/fold turn because on a cec shove i don't think that you could be called by anything weaker