1) Im fairly certain you can get in here by "dognapping" the dog. Problem is you dont get the huge materia from the submarine as you have to lose the minigame. Earns you a shiny red submarine though. woo.

2) Alexander is tricky but keep trying and you'll get it. You need to head for the centre of the ice area, after you do the minigame. Once you get there you'll find a hotspring. Touch it- its actually an option. Then start heading NE (right and up when possible). Eventually you'll come to a cave with a woman inside. Speak to her to start a fight. Beat her to recieve alexander. If you collapse you'll end up back at the base of the cliff and you'll have to go find the spring again. Use the map frequently.

3) The chest in Kalm CANNOT be opened. End of discussion.

4) You can only dig up the key to sector 6 during disc 3 I think. Just go to Bone Village and search for rare treasure. Hire as many people as possible and it should be easy to find. The only real reason to go back to midgar is premium heart.

5) To the best of my knowledge its impossible. Free exp by the sounds of it though.