There should be a field in the class info tab for Move Direction. Just need to point this in the direction you want the door to move.
What you could do is create a func_breakable around your door, and have it use the nodraw texture. Then if you plan to have the door moving, you would likely want to parent the func_breakable to the door as well so that it moves with it. Have the func_breakable send and output OnBreak to the door with the input of Kill. It may not look especially pretty, but it should give you that sort of feeling.
This one I don't really understand, could you clarify?
Not sure exactly what you mean, but do you mean that you want somebody to be using it, and have it rotate, then if they to stop using it the button rotates back to it's original position? That could be accomplished with momentary_rot_button.
Is there an excessively simple way? I'm not sure. Off the top of my head I would probably find an appropriate rocket / missile model and parent it to something that moves. Upon reaching the destination have an input/output setup so that it triggers an env_explosion of an appropriate size and sends outputs to break the objects. Perhaps some env_fire entities around to add some more effect to it.
Honestly I have not ever used this entity. When I'm trying to setup something like what you describe I just make a hollow box out of brushes, tie them to a func_breakable, and then put whatever I want inside the box.
Since this seems to be causing some trouble, I made an example map that I tested. It works fine for me. It sounds like the problem you are having is that you have it set to do the check OnTakeDamage. The way it should be setup is there is a field in the func_breakable for Damage Filter. This is where you need to specify the appropriate filter. (One thing I did discover with this was that the OnTakeDamage output from the func_breakable does not appear to be functional.)
Another thing I included in this vmf is that the box, when broken, will make a game_text display advising everybody that the box broke. I also added another game_text to display at the beginning of a round using logic_auto and having an output for OnMapSpawn sending an input for Display to the appropriate game_text. Usually I don't notice it when the map first loads, but if you toggle with sv_testmode 1 then 0, you should be able to see it.
It should be as simple as setting the key value for "Change Angles" on the func_tracktrain to the value that gives you the best result you want. For some help on this here is a vmf of a very early build of a map I was working (and gave up on) for another mod that used a tracktrain. I have put in a big grey button right in front of the human spawn that will start the truck moving if you want to see it in action. The moving truck changes it's direction when it turns or goes up one of the inclines so this might offer you some help. It doesn't look very good because I had to change the model to something that is in zps so the alignment with the ground is off, but you should be able to grasp the concept this way. (Also there are a number of extra entities in the vmf that I am admittedly just too lazy to remove, just ignore those, they won't have any function in zps).