I have made it a point to be able to set 100% conibears for beaver. I can make just about any potential spot become a 330 spot. It just depends on how hard I want to work. So yes, I will pass up spots looking for better spots. Par for the course. But if need be I can put in the work and make a good set. I block off big areas with branches, dried grass, ferns, evergreen brush, whatever is handy. You want the beaver to see that there is an obvious best place to go through to get a good sniff of that castor mound. I also like to slick up the other side of the entrance to make it look like lots of other beaver have already gone through there.

Sometimes I will throw a handful of fresh woodchips on the slicked up area for added eye appeal.

Yes they will be on bottom entering and exiting the house for quite a ways.
The beaver activity is what keeps the ice thin or open above a run.That is how you identify them.That is where you want to drop your traps.Feel with your feet(chest waders) or with a stick for the sides of the run.This will give you an idea of how many traps you can drop in there.Wider runs you can set two or three side by side.a lot of runs are only wide enough for one trap,you can set a couple or three in series along those runs for multiple catches.
Study some drained beaver ponds in summer so you know what to look/feel for under the ice.

You don't need to overdo the fencing-just enough to suggest to the beaver that the path of least resistance is thru the trap.

Educated how ? And I wouldn't recommend bait on triggers in the two scenarios you mentioned.