I'm not sure what the blinds are but in looking at the pics I see 28, 30, 9 etc. so I am going to guess those are the stack sizes. At 30 BBs or so I think min raising is fine but you can also go anywhere from 2 to 2.5x. Sounds like small potatoes but it comes into play when you get in this spot many times per month and play many months then it starts to add up. So with that, I think we can open a little bigger here but min is not bad, just probably leaving a little on the table.
On the flop, I am not sure on sizing from the pics that you used but considering we min raised pre and only got one caller I would want to build the pot. Plenty of hands
that are worse that will call like Kx and diamond draws and depending on villain BB and how well they understand the BB against a min raise you can see straight draws here as well. I think a sizing of anywhere at least 2 BBs is fine and depending on what you know about villain 3 BBs may even work here and get calls.
You check the turn which I don't like here in this specific spot. Yes, it might make Kx leery and fold but you also aren't probably getting any more at this point in the hand from Kx anyway (we don't know river at this point obviously) so I would bet here to continue to build the pot and also charge the draws. The check actually makes the Kx have no decision and the draws see a card for free. It takes away a chance for villain to bluff
raise (although unlikely) the ace and makes it harder (or so we would think) to get it all in on the river.
The river is a card that is bad and good. No draws came in and this is a board I would doubt draws would bluff so all draws villain could have would be in check fold mode. Of course now Kx will pay us off (or lead as I guess villain had Kx here... dont see any results but I am going on about 36 hours without sleep at time of writing due to traveling the past day so maybe Im missing it) so this is just a simple call as played. We only lose to KK and if villain had that then it is just super cooler.
All in all I dont really like the way you played turn since most river cards that come up as blanks will generate check/folds to you and you would then have missed a street of value.