Have a question about Successful Lineage Aspiration

[Summers]

Hello again. I'd like to have my parent sims start this aspiration but their kids are all teenagers now.  There are some quests like read 2 times to a child, so I don't think I can complete this. Will it be ok to adopt a child from computer and will it work to that child? I don't want the 4th baby now.

[oshizu]

For "Read to a child for two hours," you can read to any child--it doesn't have to be your sim's child.

The only time I was ever able to complete Tier IV of this aspiration was during a Baby Boomer Challenge.
Every other time, even when my sim's child maxed an aspiration, "Have a child max an aspiration" milestone wouldn't complete.  That was just my personal experience on three occasions, though.
Also, if your sim adopts a child, the game considers it the child of the adopting sim, but not the child of the adopting sim's spouse.

Someone with more experience can answer your other questions. 
Good luck!

[MarianT]

Unlike oshizu, I've never had trouble with a getting the "child max an aspiration" milestone. Again, you can read to any child. I've taken a children's book to the park to do this.