Just a few clarifications I may suggest.
But first I think the biggest question I would have is what type of terrain is it and how is it being used.
Is it a building, a ruin, or an impassable piece of terrain?
If it is a building that's completely closed on all four sides and models can't see in or out, most players I`ve come across would treat this as a building that would have access to the roof through the building and your models can progress to differing heights over successive turns.
As well, if its is say like a tower, as you've described, most players would assume that there are ladders or scaffolding that would a model to scale and, again, allow it to take multiple turns to move.
If its an impassable piece of terrain, then a model shouldn't be able to climb up or down the terrain, no matter how far their movement is, unless they have the fly keyword.
In my own opinion, if a model could make the climb, if his movement could allow him to go from the bottom to the top in one move, then why could it not allow him to make it part way in one movement phase and then finish in another.
A rule that you can refer to that would help explain this would be on page #2 of the primer, under Wobbly Model Syndrome.
The most important thing is however, is that you should always agree on what each piece of terrain represents before the start of a game.
Is it a building, impassable terrain, ruin, etc... Each type of terrain could have different outcomes to a rules question, if one is brought up and it saves a lot of time and headaches, if everyone makes these distinctions ahead of time.
That`s my take on #2.
As for #3, if you assume that you can move up through the terrain, then you can also most certainly charge through it. This I have done many times and had it done to my units as well numerous times. There can actually be some pretty unique situations in this case. If your units are climbing within a 4 walled piece of terrain i.e. you can't see into it, then those units cannot shoot out of it, as well as units cannot shoot into it. This is what some players refer to as a 'magic box'. The beauty with charging a unit that is on the roof of such of these pieces of terrain, is that the unit you are charging cannot fire overwatch at you, as they do not have line of sight. The same would go if you charged a unit through a ruin, to assault a unit on the other side of a wall. As long as there was no line of sight, your unit is spared overwatch.
#4 I completely agree with, but to clarify again with my experience, a unit does not have to be wholly within the terrain piece, only contacting the terrain piece. I know this may be construed as rules semantics, but any games I've had with experienced players accept a model touching a piece of terrain as being in cover. As long as all the models of the unit are either in the terrain piece or their base is contacting it, then they are considered in cover. Don't want to get into a rules debate on this one, just wanted to point out how I've also experienced this.
#5 Again depends really on the terrain and is up to interpretation. I've had a player completely take up every inch of a 'magic box' roof with sniper models and I've had a painboy able to assault up through the box.
These rules are tricky and I've heard different variations of answers when I've heard them ask. These are just my experiences with these rules in question.
Unfortunately GW never made this game's rules with tournament play in mind, even from the very beginning, and always said to look to whatever makes more sense to both players and if you can't agree to roll a dice.