First, is there a simpler way to seal the lenses? Like some kind of foam strips I can use instead of the horrible sticky rubber? That would make things a lot easier, especially if I have to ever open them up and adjust the projectors in the future!
As far as best, and easiest to deal with for re-work, Butyl rubber is the way to go. Doesn't get much easier than tossing the assemblies in the oven for a few minutes, and then pulling them apart. It's all reusable so you don't need to reapply. Plus, you've got the LT headlights, less work than the LS/SS models.
Next up would be RTV silicone, that's what I used on my first retrofit, when I had to cut the headlights open. Rework wasn't too difficult, just needed a razor blade to cut the RTV, and then reapply a little bit to reseal it later.
I don't think foam strips would work very well, for very long. Think of it this way, on the doors, lift gate, and sunroofs, you see rubber seals, not foam ones, to keep them water tight. With all the hard work and time you're putting into this mod, I think the last thing you want is a bunch of water in there.
And second.... what's the best way to align a projector headlight? The aim I mean.
The answer to this question is subjective. For me, it was easiest to remove the headlights from the truck, secure them in a work area facing a wall. Power up the halogens and mark where the hot spots were on the opposite wall with tape. After retrofitting the projectors, and before sealing up the lenses, put the headlights back in the test positions, fire up the HIDs to see where the hot spots and cutoffs are. Make rotational, horizontal and vertical adjustments as necessary so they line up with what you had before. Seal them up, reinstall on the vehicle and enjoy.
I know what some people do, if they have the room, and a 2nd vehicle, is leave the lights on the vehicle, park it in front of a wall, and repeat the above process. That wall should be 25' away.
Now if you never made any reference marks to compare to, you're not SOL, but will just require some work. Here's a video from TRS on how to fix your alignment if that's your scenario.