Is it a good gameplan in these situations to check all of our range (our bluffs also) on this type of boards? And bet on lower ones?

fold pre

vs a c4bet

We have to call pre due to the awful sizing of the cold 4bet but I like just check/fold flop even though we have a gutshot and BDFD.

As played, I love the turn lead and sizing because if our opponent does have a hand like AA, or KKK he's always going broke as his pre-flop sizing demonstrates he's probably a very weak player and very weak players don't do very well when it comes to folding big pairs.

Fold to the open raise is my move preflop versus what looks like a tighter reg type. After we call I like check/folding flop because even if we hit our hand we run into AQss too often at best.
The only saving grace here is what RegiTime said, in that leading when we hit is good as these tighter guys won't be folding an overpair or a set any time soon but may (or not of course) slow down on a tricky runout.

I'm not as good at explaining my thinking sometimes though.