[MarkD]

with all those low cards and a BB defender, I feel a check-raise coming most of the time.

I think this is important.

So between hand 1 and hand 2 it apears that you are more afraid of a check raise in the first hand because of the very low board and this sways you from betting to checking (since hand 1 and hand 2 are similar in terms of number of outs).

It also appears that you think we need to fold the river unimproved in both these hands if we get check raised. I think this is probably correct.

In hand 3 there is almost no river card we can be comfortable with if our opponent bets into us after we check through on the turn. Combined with the number of draws on board and I think this throws the decision to check/bet towards betting but also think we are in a very bad spot here once check raised. We have to be good a little over 25% of the time which seems like a lot if we get check raised. (This doesn't include the times where we are ahead on the turn but he draws out on us on the river, so I would increase this percentage to over 30%). I think if we get check raised in hand 3 we have to fold, but I hate it. Actually, it's probably correct for us to call the turn and fold the river since we would be getting around 7-1 on the turn.

Maybe there is a general maxim for these situations such as: It is incorrect to call on the river unimproved after calling a check raise on the turn. (I'm certainly not convinced of this but think it's highly probable even though we would be getting 9-1.)