No. F-35A is conventional take-off and landing. F-35B is STOVL. F-35C is CATOBAR (catapult take-off, arrestor landing).

Army, Marines, Navy?

Air Force. The Army doesn't operate the F-35.

Heh, I meant to say Air Force, can I get away with saying that they used to be part of the Army?

Didn't think so :)

Not this variant.

I have no idea how VTOLs would work in this scenario, but I suspect it could be recovered safely in that config.

Non-VTOL fighter landings with improper gear configurations have various guidelines (As discussed in the report here) in their checklists, depending on which gear are down. They range from landing normalish, landing while applying counter-forces etc, to approach-end-resentment, to ejection.

IIRC USAF does not use the F-35B, which to my knowledge, is the only VTOL capable F-35 variant.

The F-35B is the VTOL variant.

The Air Force doesn't fly the F-35B, they fly the F-35A.

Not the A variant, which is what USAF flies.