As to your questions.... yes. To both. Yes, encourage. BUT... not at the expense of closing other doors, or tying identity to those particular hopes.
This.
I know quite a number of young adults who currently attend Ivy's and top tier schools. These schools are not impossible to get into especially for a gifted student but it does mean taking the most rigorous classes (typically lots of AP's) and getting top grades, and having interesting extracurriculars. If this desire is coming from him, then he will be motivated to jump through all the hoops.
In my case my husband went to top tier/ivy schools but I have no illusion that my DS15 will manage get accepted at either university despite the legacy. My son is not motivated and it shows in his grades. We have been discussing what grades he needs to attend top public research universities. I am assuming that he will do well on the SAT, and it looks like he will mostly likely be interested in math/computers/engineering or science at university.
