The F-117 is a low-flying ground attack aircraft. The B-2 is a (very) high-flying strategic bomber.
F-117s and B-2s cruise around the same altitude, 30,000 to 40,000 feet. Not particularly high. Same as commercial airlines.
The SA-3 battery that shot it down only locked onto it with radar when it opened its bomb bay doors during a strike
Incorrect, they had tracked F-117s on the same flight path over the course of several says. The Serbians were also monitoring NATO comms with their AWACS; "At times, they acted like amateurs," said the battery commander.
and one missile got "close enough" that its proximity fuse detonated
Which is the primary terminal use-case for SAMs. Very few are designed to hit the target ( Rapier is one such example ).
As a result of the loss of control, the pilot ejected, and was later recovered by a Marine rescue unit.
Mission kill, SAM battery succeded. USAF failed.