Hand 1
We are definitely checking here OOP multiway. We are facing 3 different ranges and when we get called by one villan, we have no idea where we are in the hand, and when called by 2 villans or more - its a nightmare. I know we are UTG and have alot of Kx in our range, so do some of the callers behind, as well as some middling pairs that just can't fold in position to a single bet on such a dry flop. We get alot of honest responses multiway and blindly cbetting range here will effectively light chips on fire for you long term. The only good thing is when the Q comes, not only does it give you a gutshot broadway draw - but more importantly it's a great bluff card to actually get those middling pairs to fold and will likely polarize our villan to a Kx, or possibly a strong Qx hand. So by barreling turn we get those middling pairs to fold, and then we can decide whether or not to shut it down going into rivers.
Learn these multiway spots - tons of players are making massive mistakes here - studying these will net you tons of chips long term. Few rules of thumb multiway -- we are checking OOP overall around 82% of the time, only cbetting overpairs, 2 pair, middle and bottom sets. We have no bluffs OOP multiway. We only raise 2 pair or better multiway, and again, when we raise we have zero bluffs.
Hand 2
The cbet vs the BB defend range is more than fine here, standard and I like it alot. When the turn pairs the 2nd or 3rd card on the flop, its a GREAT spot to double barrel - puts a ton of pressure on top pair holdings and gets alot of folds. I would double barrel turn with a large bet of 60% or more, and with the intent to triple off the river when the flush comes in. Why? That's how we get a Qx to fold and we have no showdown with K hi.
As played, I don't like the bet-check-bet line. What are you representing here? A flush? A Qx hand you decided to pot control the turn with? You certainly don't have a J, you would've value bet - your Qx isn't very strong, or you would have value bet turn...most flush draws are unpaired and will continue firing turn to build a pot if they hit, and to give themselves a nice spot to bluff if they miss. So all in all...your story doesn't make sense.
What are you trying to get to fold by doing this? If I were your villan here, i would call you off with any 6x and all the middling pairs as well like 77s, 88s, 99s, etc. --- and if I had a hand with no showdown value, after you check turn I am bombing river when the flush comes in - and if you do have a Qx hand, I will make your life miserable and even if you don't fold, you will at least be considering it.
At the end of the day, your story has to make sense. Villan could've floated flop with T8, 9T, 89, KT, AT, etc - its not always a pair or a flush draw - don't fear the reaper. Understand betting sequences, what they will tell you about ranges, pick your spots and play the game.
In a nutshell that's all I did here - i deduced if I were your villan that your turn check means a weak Qx or middling pair at best, and if I have showdown value I am bluff catching - and if I do not have showdown I am leading river with a large bluff of my own targeting those holdings and better hi card hands that I cannot showdown against.