There is a sprout, and they take either it or another seed to the Trann Dome (I'm assuming it was another seed, since sending your only food source across a waste land would be very stupid, but I never really checked).
As for the trees on death mountain, a few of the smaller ones do appear to have some stubborn range leaves attached to them so they may have died somewhat recently (I've heard that some people believe the mountain to be Lavos' shell, so that would help some to explain why they appear to be the only plant life obtaining nutrients).
And back on the topic of the gates, I always thought that the Red gate was important because it took Lucca to a very specific point in time, by contrast to my thought (I'm new so I'm a little hazt as to the standard belief in this) that the standard blue gates took you a set distance on the timeline, like 400 years to the minute (Till they start taking you to the end of time, where there really is no time.) I usually just chalked up the green gate to Lavos interference.