1. You can get them adopted by someone else, in particular if you bring a kid back to someone, while they are still in OMGSUPERHAPPYMODE you can get them to adopt any number of additional kids, I tested and had a human lasher who I reunited with three of her kids agree to adopt another 60 or so assorted dorfs and humans... no elves because I'm not rescuing them, we're at war for a reason.
1.5 Ask her to wait somewhere for you, travel away and return, she should be listed as a recruit, you can give her weapons and stuff at this point and she'll begin behaving accordingly.
2. Uhhh, you can tell it to wait outside a town, but I don't recall it freaking people out too bad actually.
3. Yes changes you make it a world will carry over to fortress mode and vice versa, when I started my first adventurer it was with a dorf from my own 5 year old fort, said fort was made in a site which wasn't originally at war with the gobs, it was by the time I started adventuring, but the nearby goblin sites were emptied by my actions in fort mode and severely depleted by what I did with my adventurers, though I did incite several other wars and saw multiple side battles between different goblin civs!
4. No but you can claim it for your own group, sadly you can't make one over-arching group to claim sites with, it's a new one for each site sadly. As long as you are in the throne room and nobody else with a potential claim is present or alive you should get a text box saying you are now in control of that site.
5. They get the fame and you can regale others with tales of their deeds, I think you get a bit of a boost from it but honestly nothing gives as significant a gain as rescuing kids which only you can do (the difference being that any number of dragons and rocs and demons and goblins will only ever get you legendary hero and/or legendary killer, but a few kids returned home will lead to you being greatly respected for heroic acts and after enough of this you begin to get recognized in different sites!) but it's still nice to tell others what they've done along with your feats.
6. I use dfusion > 2 (adventurer tools) > 2 (change adventurer) to do it myself, though I suggest editing the person you want to control and adding reading skill if you already have it yourself, if just because it is nice being able to read signs and slabs and books, whether you want to become a necro or not, there is no way I know of to add reading skill to someone you control, but you can do it to someone you are going to dfusion swap to.