1) Yes adept or higher parents (dont have to be check as parents just need the skill required even if you have them on somthing else at the time) drop the adult with the proper skills on any child and watch them line up. children do not learn skills by this some people have speculated, but its not true.

2) Your options for this are, if you have a female over the age of 50 she cant have anymore kids so you can continually put them together and not worry about new children, dont wait for them to go to the love shack, just pick him up and drop him on her over and over again, and depending on how far he is allready, should take about 3 minutes of this, another option for this is the adult who has parenting skills that is *teaching* the children does gain parenting skills but this does take longer then the option i mentions before.
His healing skills requires a little patience and time, you can either a- place him over and over again on a herb and wait till he *improved his skills* or you can make one of the *special ill stews* and make him heal a bunch of people, i would go for the study herb one, seems less mean lol

3) yes when their worried about food they do seem to move slower, but be patient when you solve the algea problem they will have unlimited food.

4)yes they gain skills by examining and fixing huts, there are 3 reg huts, plus the love shack and sewing hut and hospital and there are also 3 other ways to gain building skills, clearing brairs and mosaic and vines, if you have all those, your villagers will still gain skill on examining and fixing huts,
I havent seen any evidence stating they gain skill from the fire, but i could be wrong. usually itll tell you they are gaining skill when its happening, and i have never seen that.

5) no the kids dont pick up anything without you moving the hand of god and placing them on the item, sorry.

Hope this helps, if you have any other questions you can PM myself or anyone else thats ususally helpfull, like Charley or village_monk, etc... we all post alot so you know which ones.