Re 3), yes it had, but for one thing the US Silent Service was mostly deployed in the Pacific (where they did a number of their own on Japanese merchantmen), and for another in that day submarines were not the answer to submarines. Destroyers were. The primary weapons of submarines were torpedoes and their deck guns, both of which were ill suited to destroy targets that were low on the water, manoeuvrable and with small surface under the water. Remember, they didn’t have today’s homing torpedoes, what they had were (malfunctioning) dumb fire motors with a bomb strapped to it.
Nor were submarines any better than surface ships at finding other subs: today subs are indeed better because they’re submerged 24/7 where they have good acoustic conditions for their passive sonars. In WW2, submarines spent most of their time on the surface, submerging only when they were about to blow something out of the water or when they were being attacked.
As for anti-sub aircraft, before the advent of radar they weren’t very effective either: too much ground to cover with a Mk1 eyeball, too little warning of attacks and not enough boom on board either. Basically their only chance was to surprise a sub on the surface and bomb it before it could dive. Which essentially meant one hasted bombing run on a small target where the pilots were as surprised as the sub crew (not to mention, U-boots also had AAA guns of their own to disrupt straight bombing runs).
As for why the US didn’t deploy swarms of destroyers on its coasts, well, they didn’t really have time to, nor did they need to in the end: yes, Germany deployed a handful of U-Boats right off the US coast at one time (Operation Paukenschlag/Drumbeat - the US had already declared war by then), but they didn’t repeat the experience and the offensive didn’t last long because resupplying the subs all the way out there proved to be just as much of a headache for the Germans as finding them was for the other side.
It was worth it as a surprise operation, but once the US figured it out they did deploy anti-sub measures and the operation was canned. U-boot captains got a couple months of happy, uninterrupted hunting and that was that. Back to prowling the Atlantic.