I don't know much about domestic or private adoptions since we did an international adoption but many agencies handle both. We used Gladney for our adoption from Vietnam & I know several people who've worked with Spence-Chapin. They've both been around for a long time & have good reputations. There are tons of others of course but those are the two in NY that I, personally, know the most about.
Regarding your ages -- it really depends on the country's rules and on your agency's guidelines. For instance, my understanding is that the U.S. has no maximum age for adoptive parents but many agencies impose their own limits. Often these guidelines are more flexible for special needs children though. You should check check
RainbowKids.com Adoption Information, Support, Child Photolistings, Articles and Resources to get an idea of the country guidelines and then check each agency's website to see whether they've imposed stricter limits, etc.
Regarding doing fertility treatments while pursuing adoption -- that also depends on the agency and on the country. Some of them are fine with it, some have the caveat that there must be a year between children (adopted or bio), some of them won't allow it at all. You'll have to speak with each agency individually to find out their stance -- I've never seen that particular info. on any of the agencies' websites.