Happy birthday, Scott.
1. I'm finally getting into Octavarium (the song.) It's growing on me... I hated the opening Jordan jerking off part, but since someone said it's his "ode" to Pink Floyd (Shine on you crazy diamond) I get it more... I've listened a few times and it's growing on me.
It really is a fantastic song. But at the same time, it really is a bit much for a new fan to take in. For something that long, just give it time to grow on you. You might also really enjoy live performances of it. Have you checked out Score? I would recommend buying it and sitting down to watch it.
As far as the opening of Octavarium, I really love it, despite that it can feel like kind of a chore to get through when you are wanting to get right to the song proper. But it is such an atmosphere builder. Since DT have never been shy about hiding their influences, even very specific influences in their songs, I always thought it would have been awesome if they did the four-note B♭, F, G, E progression from Shine On in live versions of Octavarium. Maybe some day.
4. I'm kinda bummed how late to the party I am... and I know, always welcome... however, it sucks to know how much awesome music I'm liking that I'll likely NEVER hear in concert. I hope one day I'll get Dance of Eternity, but that's more likely than songs like In the name of God, ITPoE, Octavarium even... I don't see them playing shows in the next few years and playing some of these older epics... or even something like Stream of Consciousness.. I wonder if MM even knows any of those types of songs. I know he learned ANTR for the tryouts, so since he learned it, why not play it? I looked on setlist.fm and they haven't even played ANTR since the last MP tour. C'mon guys.
Well, the thing about DT is that they are REALLY good about trying to rotate almost everything in at some point. REALLY long songs and ballads are a challenge (long songs because of the amount of set time they eat up, and ballads because you can only play so many, and they usually have a couple of new ones each album). So it wouldn't surprise me if ITPOE never came back again in full. But I think they know how revered Octavarium is, so I would expect it to return at some point despite its length. I think the others that you mention are also pretty likely at some point. You just have to be patient.
The other thing is, there are really good live performances of most of those songs captured on the band's live releases. As I posted above, if you haven't started checking some of those out, you might want to think about it.