Speaking from some (very) recent experience.....
1. It's the same F35 mock-up that was on the Ship for Meet Your Navy in July, and again for the recent London visit. Couldn't crane it off before sailing for the VAAC trial due to being at anchor rather than alongside.
2. It will go down the lift - it was in the hangar for some of the receptions held in London, and was kept in the hangar for the duration of the VAAC trial, only coming back up Thursday morning before Lusty's return to port.
3. It does have lashing points (of a fashion), but nothing you'd want to trust in a Sea State 6.