* Do you get the water out of the pressure-plate area by just removing the construction wall?
* Would pressurized water flow allow you to push a FB down onto the next level and therefore directly onto a webbed cage trap?
Answer 1: Exactly. To reset the trap after you have removed the contained FB, you would remove the construction to drain the pressure-plate tile, replace the doors and floodgate, then refill the water chamber above the cell.
Answer 2: I don't see why not, but I also don't see why you would want to. Once you use the cell's manual release, so long as the way back to the caverns is shut he will path straight to your fort... right into a prepared webbed cage trap. While positioning a FB or a GS for a single webbed cage trap is straightforward, doing so for a webbed cage under each hall would be problematic and a micromanagement nightmare.
However, web on trap -- how do you make that portable?
And does having a web automatically make an FB get webbed in the tile?
I thought the webbing part happens at the time the web is spewed, causing a temporary stun, that can allow cage trap to catch.
A web will stop, however briefly, any creature capable of being webbed should they stand on it. A dwarf carrying a cage to reload a cage trap will have the job interrupted if they wander into a web. It is that minute interruption that allows a cage trap to activate. It will not, however, work on any webbing clown, titan, or FB. Also note that any of the above that is in the shape of a spider can web by default, even if not stated in the description.
While I have had great success with it, I have also recently run into a few problems as well. It all comes down to the doors in the hall and oddities with building destroyers.
In one case, I had a FB bypass the floodgate to stand by the door and do... nothing. Building destroyers need 1 tile (or maybe a diagonal?) between them and what they are destroying. This FB wanted to destroy the furniture, but would not move to do so. Trapped? Yes. Could not remove for caging, however.
In another case, I had a FB destroy the floodgate just fine, but had the resulting water pressure push it against the door it was trying to destroy. Result: again, a stuck FB.
I'm currently pondering putting the doors 1z up from the floodgate. Or if I could replace the floodgate with one of the doors. OR combine both, make a vertical U out of it, so they go down, destroy door releasing water which closes the bridges before they can climb back out. But I am also pondering if this automated trap is even necessary anymore. With the 'Do Now!' feature of levers, and enough doors in the hall, the manual version should work just fine so long as you pay attention.