Not that a +/- 3bb spot isn't worthwhile, but all that effort could probably be used in a lot more worthwhile spots I'd imagine. This type of spot really don't come up all that often (checking all the way down, 4 flush turn/rivs).

It's fine to bet here once in a while, its fine to check here once in a while. Sometimes you have SD value.

The biggest part of this hand missing value is pre-flop imo, if you really want to find the value here.

As played I would also bet flop.