Takin into account the hundreds to thousands of trees necessary to build ships depending on size plus the wood needed for charcoal to smelt iron plus the use for buildings and firewood....we will run into a timber crises in 10 turns or less.
Not really... There can be hundreds of thousands or even millions of trees per square mile, which means there's hundreds of millions or even billions of trees per province. That's part of why it takes centuries, not years, for deforestation to happen with pre-industrial tech. They don't use wood efficiently, sure, but they can't use it all that quickly, either.
"The Hunt rides. The Hunt protects."
There are only certain types of tree that can be used for ship building and only a small percent of those are large enough for shipbuilding. Then you take into account that they can only safely cut in about a mile radius without being eaten by pixies and dire bulls and vampires and untold number of creatures. So there are 640 acres or so in a square mile. So divide that by the 70 acres it takes to build a ship and that’s 9 ships per town minus woodnused and exported for buildings. Now the lumber jacks are still getting attacked and so they are leveling up and should be able to cut deeper but these are most likely the citizens that make up the units that spawn in random events and they get killed. So that keeps it at a small radius they can safely cut. So sure there may be enough trees but we can’t get to them.
Concerning sending LT's on someone else's adventures: I assume a LT can lead an army doing a war action, but does the rule mean they cannot do that if the war action is against the units in another regents realm (due to an event)?
I know you have to spend an action, but question is does the new rule prevent them from doing that if the battle is to solve a special event of another regent. Also I think a LT can lead an army if you spend a domain action for it as well.