I can't tell which boat it was - but then again I'm not sure how much is some sort of stock footage or actual footage taken over the course of the CQ evolution.
At least the part filmed at 4+23 is on the USS Nimitz (CVN-68). You can see it to the left of the screen as the airplane comes to a stop.

Good question about the LSO not telling a guy/gal their hook isn't down.
I know it happens
I notice at time 3+45 that the hook isn't down and the AoA indicator is steady.
In my former airplane, with the switches set appropriately, if the hook wasn't down (for instance a purposeful hook up pass) the AoA indicator will blink. If I remember my time on the platform too - there is a guy with binos looking at each airplane at the 180 deg position and relaying the configuration of the aircraft.

On one personal note - the young Marine mentions around 5+40 that the "cockiness came out" on the second day. I can relate. On the second day of my TA-4J CQ period I was feeling *salty* and ended up throwing a Wave-off in the groove pass on my second to last attempt. That is a 1.0 GPA pass if I remember correctly (back me up here any LSOs). Dropped my CQ GPA from 'doing pretty good' to 'whew - glad I didn't mess up twice'!