I will use sending exercises around the mounting block, eventually bringing the horse to stand next to it, but not standing on the block yet. I want him to get used to the concept of just standing near it quietly. When he will stand next to the block or whatever I choose to use as a mounting block, I will then start standing on the block, and start doing sending exercises again, eventually bringing the horse to a stand still next to the block, and then rubbing him, patting the saddle, banging stirrups and what not (should note that I would have also done prior desenstization with saddle, ropes, etc, before moving onto doing them with the block...). If the horse moves away from the block at any time I will just resume sending him back and forth near it, and eventually bring him to rest next to it again. Basically I use a approach and retreat type method, and teach the horse that standing next to the block quietly no matter what I do to him there, is easier than having to move his feet. For each horse it may be different, timewise...some may take one 15 minute session to really become solid, and others it may take several sessions to retain what is being taught.
#2... For this one it's going to depend on whether the horse has had prior issues before. If it's just a young horse, and has no known issues, I will simply just start riding off; short distances at first, and gradually longer. Usually if the horse is comfortable with you as his leader, you really should have no issues ever. The key is to be consistent from the beginning in what you want, and establishing respect from the ground up.
Now, if a horse has issues with leaving the barn already, I will start with gaining his respect from the ground (in case I have to dismount to work him later...I want to know he's not going to run over the top of me, or try to kick out at me). Many times, if you establish respect from the ground, a horse may not even attempt his prior 'barn sourness' issues, as well...especially if you have a good solid 1 to 2 weeks JUST to spend on ground work. However, like some horses I've worked with, ground work and gaining respect from the ground, isn't enough. So if it isn't start by riding a short distance away from the barn or corral and stop him before he gets antzy pants, let him rest there for a few moments, and take him back to the barn. If he gets antzy, or rude about going back to the barn, then take him back there, and put his butt to work...HARD! If he wants to be at the barn or corral, then make it extremely uncomfortable for him by working his tail off. When he is panting pretty good, move him off a short distance away from the barn and let him rest AWAY from the barn. You are basically retraining his mind to want to be away from the barn when you are on him, rather than wanting to be at the barn. If being at the barn means hard work, he will figure out quickly that being at the barn is not a very fun place to be. Oh, and if he is one of those that tends to get snarky about being worked at the barn, get off, and work his tail off instead...either way, the barn has to be the unpleasant place to be, and he will soon figure that out. But you have to not be afraid to make him sweat...really...the harder you can work him at the barn, the quicker he will "get it".
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."