@ClayMask, I can't answer all your questions but:
Regarding adopted children, they seem to be handled just like biological children. Perhaps the better distinction would be related/unrelated to the parent(s). Unrelated would be like inviting an elderly gardener into the household and having that gardener adopt a chlid.
"Have a child max any skill": This can be a childhood skill. Earlier today, both parents got credit when their biological child maxed the Creativity skill. Mom switched over from a different aspiration and still got credit
"Have a chlild complete an aspiration": Tier 3 of Successful Lineage has the "Have a child earn an A in high school" requirement, so I've had the same high school kid work on an "adult" aspiration.
@CynKuy, regarding "Have a child reach the top of a careerr," I read on another thread on this forum that this requirement triggered for a teen career, but I haven't tested it myself.
Wish I had better answers...I guess this aspiration really calls for test playing because of the ambiguous wording....
I'd like to correct erroneous info I'd posted before.
The Family aspirations don't treat biological and adopted children equally.
Recently, my founder adopted a son. When the son maxed the Mental skill, the "Have a child max any skill" triggered for the founder but not his spouse.
I completely forgot that the former "Adopt a child" requirement (now gone) worked this way too; it only applied to the adopting parent.
The "Helping with homework" and "Read to a child for 2 hours" requirements apply to any child in the household.
Gah, I feel like I'm pedaling backwards....