There is only one timed quest; in Verdistis, if you agree to commit arson, you must do so that game day or someone else will get to it first.
The other quests you mentioned do not have a time limit, but are effected by the completion of other quests. Basically, completing later main plot quests can force the updating of certain NPC status or locations, which would have been done by the completion of earlier main plot quests.
1 a) I don't recall mention of Verlat failing to show up in Verdistis if you healed both soldiers. I did most of the quests in Rivertown and explored pretty much everywhere reachable (without going to the castle) before entering Verdistis, and he was there.
1 c) If you complete any of the 3 quests that give you an invitation to the castle before you complete the escort quest, the healers will move on their own (and if you had not healed the 2 soldiers, those quests will also fail).
If you skip restoring Mardaneus' sanity, his status will also get reset, but I am not sure exactly when (somewhere between getting an invitation to the castle and scrying for the human council member).
2 d) The dragon belt in Verdistis is relatively easy to get to. However, stats on equipment tend to be better at higher character levels. Poor equipment is always going to be poor, but with a potentially powerful item, a higher level character is more likely to get random stats in the upper range of what is available for that item.
3) I don't see much point to activating some of the teleporter pads early. Wouldn't it be less effort to activate them as you explore, than to put off early stuff to activate some of the teleporters, then go back and do the early quests, then return and do the later stuff?
If you want to run around and level up early, though, you might as well activate any teleporter pads you can get to.
