1)
Your level goes up by one whenever you level 10 majors total. So 1 sneak 2 blade etc up to 10 grants another level.
it depends on how LOW your majors are when you start. If you are a combat character then combat majors start out higher (so max level is lower). If you have a racial bonus then the major starts out higher so max level is lower.
One thing to keep in mind for this question and others is that monsters increase in power in response to your level. So if you are 47th level you will fight some powerful monsters!!!
If you want to be the highest level pick say combat but choose all majors that are NOT combat and a race that has none of your majors as bonuses.
2) by big gate I don't know if you mean the first oblivion gate or something later in the plot I haven't gotten to. I try to get sigil stones that are useful and also roleplay (so I don't go in a gate at level 2).
3) I don't know if you mean a certain weapon or a type of weapon. I like to use a shield because then the wear and tear from blocking and attacking doesn't damage only my weapon. I like light weapons so I can carry more for different situations. Definately a longsword for high damage to kill routine things and a dagger for backup and fully charged up. I don't like blunt trauma as much as razor sharp blades
