1. Right, it is a fortification, so it should grant a 3+ cover save if the respective model is covered at least 25% from one or more firing models, regardless if the shields are up, or not.
2. Nope, look at page 99 if you don't roll enough to get up in one go you don't go up at all. It's all or nothing with climbing.
3. Yes, skimmers are units and every unit that stands upon a shielded Skyshield Landing Pad gets a 4+ invulnerable save against shooting. They don't have to be actually covered, because it is no cover save.
I must rule with eye and claw — as the hawk among lesser birds.