Great advice from Brian. I will try to answer the specific questions about rhythms. I've loaned out my music, so I'm answering from memory. If I make mistakes, hopefully someone will jump in and correct me.
1. downbeats: I'm not sure what you're asking. Are you wondering whether to play on beat one? No, you wait for it to go by. Breathe in on beat one, like you're going to sing, but don't play until after beat one.
2. triplets vs. eighth notes: The tricky thing about this piece is that some of the eighth notes are longer than others. In 9/8 time, normally the eighth note gets one beat, right? In this piece, they are little quick beats, the triplets that you already know about. But when you see eighth notes that have a little 2 written above, or when the eighth notes are in groups of two instead of in triplets, those eighth notes are longer than the triplet ones. The heavy feeling at the beginning of each triplet is the "big" beat. Most of the big beats get split into 3 parts to make triplets, but in the other places, they get split into only 2 parts. You have to stretch those out a little to make them fill up the big beat evenly. If that answers the question for you, skip to #3 below. If you're still not sure what to do, keep reading.
Tap your hand on all 9 beats of a measure (over and over). This is the triplet feeling that you know. Keep tapping and count out loud: "One-and-ah, two-and-ah, three-and-ah" (do this instead of counting to 9). Now keep counting the same but only tap when you say "one, two, three." Then only say the "one, two, three," the same as you tap. These are the big beats. You have to feel them strongly, because they get divided different ways, in 3's and 2's. Next, you have to practice how the 3's feel next to the 2's. Tap your slow beat and say "trip-ah-let" on each one for a while, so every beat gets divided into 3 again. Keep tapping the same speed (use a metronome if you have one) and now say "du-ple" on every beat. Duple just means something is divided in two. You'll be saying "duple" more slowly than you said "trip-ah-let" in order to use up the whole beat (say it evenly, so the "du" and the "ple" are the same). Keep tapping, and say "trip-ah-let, trip-ah-let, du-ple, du-ple" and change back and forth. Now... look at the first two pages of your music and find all the triplet patterns, then all the duple patterns.
3. free form: Brian gave an elegant answer to this. Free form is just how you feel the music, going a little faster in some places, slower in others, but as he said, first learn it in strict form, playing exactly in time. Many people don't do this, but if you do, you will sound better than they do!! And you will understand how to read complicated rhythms better than many people.
4. duples, ms. 14: Big beats cut in half like you practiced above.
5. It's just the big beat divided into 6. I can't remember exactly what the RH does here. I think it has duples. So you can take each note in the duples and make a little triplet out of that, and feel your 6's that way. That would be counting each group of 6 as "1-and-ah, 2-and-ah." If the RH is in triplets, then you can feel each 6 as 3 little groups of 2: "1-and, 2-and, 3-and." The music will sound the same either way, because the fast notes will be at the same speed either way. But one way will make it easier to match up the hands together, and you will feel more solid and strong. So just see which feeling goes with the RH in that section.
Hope this was helpful. Good luck! Let us know how you're doing.