a) Can any other age than kids visit Camp Gibbi Gibbi? And - can sims visit runaway (Getaway?) retreats from the map like they visit any community lot, or is the only access via ordering a getaway stay on phone/computer?
Any age Child+ can be assigned to Roles for Getaways. You probably need at least one Teen+ Sim to supervise, but haven't checked yet. Getaways can be started via Phone (now) or Calendar (now or planned for later), but I haven't checked the Computer yet. Custom Venues can be visited straight from the map, but you won't be on a Getaway that way.
b) I like the new feature where certain activities makes a difference to a grown up, such as a child training Archery will become more focused later in life. Is this feature limited to the new skills, or will there be general changes, basegame, too?
There are many. I need to make a post. There are tie-ins to lots of careers from many packs (Scientist, Doctor, Law, Engineering, even part-time and freelance careers etc), but likely some still missing. Some boost skills, some have Mood effects like the Archery one. Others effect Fame or weather effects on Sims.
You get one for free on Teen+ Sims via a self-interaction, but can also get them all in the Reward Store for 100 SP each - you can browse the possibilities there.
c) Is any skill affected by Kayaking? Are they performing this new activity the same, regardless of experience/fitness etc?
Kayaking builds the Fitness Skill. I haven't done it enough to see if it changes with progress, sorry.
d) Will the new Diving come with a score (like bowling does)? I'd love to arrange a diving contest :) Understanding there is a new Diving skill, but would like a way to tell one dive from another, quality wise.
This is another skill I haven't used much yet, but didn't notice a scoring system in play. They have amusing fails though, and fail less as they improve according to devs. I do know Crinrict was all-in on this skill, so maybe check out her post?
Crinrict's Diving Skill Blog
e) I think I read that the papercutting skill/activity is for all ages. Is there any top product that only those very skilled (or grownups) can create? Like Japanese oragami?
You start out with a few paper colours creating simple origami like paper planes, paper butterflies, and some goofy-looking paper maché models. You get more paper colours and craft types as you level up. You can also make origami from money.
I haven't maxed this skill yet, but I know it's used in getting the final butterfly for your collection. A magical origami one made alive. You can also make functional greetings cards that can be inscribed with a note and gifted to Sims (think TS2 notes from dates, but more personal).