Here are my thoughts, just remember that they are from a layman, and someone who has also struggled with Orthodoxy (though my struggle has been between Orthodoxy and agnosticism)...
* I love the Catholic saints I have come to know. Can I, as an Orthodox, privately still venerate them? For example, St. Francis, St. Anthony, St. Dominic, Blessed Teresa of Calcuta.
Most of your questions are tough ones, I think. With this one, I think of St. Isaac the Syrian. So far as I understand, he was not in communion with Orthodoxy, yet we consider him a saint of our Church. Does this mean that there are saints outside Orthodoxy? That we can venerate people outside Orthodoxy if we are Orthodox? I don't know. Certainly there is nothing wrong with loving and respecting someone outside Orthodoxy, and looking to them for inspiration or insight. But veneration in your private life? I don't know. I would say that it's ok, but that's just me.
* There Marian apparitions, which I love. Can I, as an Orthodox, privately still acknowledge them?
I'm not really familiar enough with these to give an opinion on them. I know that Orthodoxy has had Marian apparitions before, as have the Oriental Orthodox. But most Orthodox seem to take a dim view of Catholic apparitions, for one reason or another.
* I do love the Rosary. Can I still pray it?
Yeah, I do believe that some Orthodox pray the rosary. Either the rosary, or something extremely similar, I forget which. (here is a list
of threads with a "rosary" tag).
* Will I feel (culturally speaking) at home in an Orthodox Church? Which jurisdiction would be most appropriate? I’d like to see the OCA become more than it is. I am, after all, American.
I only know that I do feel at home, in spite of me being very Americanized. I've been to churches and monasteries of a half dozen jurisdictions, and I only ever felt out of place once, at a parish, and even then I went to a monastery from that same jurisdiction and felt totally comfortable. And who knows why I felt uncomfortable at the parish, it could have just been me for all I know. That's not to say that there aren't some... less than welcoming parishes. I'm just saying that, in my experience, Orthodox people tend to be friendly. Maybe they aren't as gung ho about making you feel welcome as a "seeker sensitive" Protestant church would be, but there still aren't many roadblocks to feeling at home, IMO.
* Because I believe in the validity of Catholic Apostolic succession and Sacraments, do I have to give up that belief to become Orthodox?
Well, I think that's the toughest of your questions. Many Orthodox would probably say that you should
, and some would say that you have to. Is it absolutely necessary? In my mind, that is the sort of thing that you could struggle with while being Orthodox, if--and only if--you believed that Orthodoxy preserved the pure faith once delivered to the Apostles, and want to fully commit to Orthodoxy. But it might be a hard walk, and some might suggest that such an approach would be a recipe for disaster. I suppose this question, as with all your questions, is really something to discuss with a good, pastorally-minded priest.