Each player may create an unlimited number of magi, of any age, following standard rules of advancement after gauntlet. They may only have one magus per covenant, with no limits on the number of covenants they play in.
Each player may have one companion per magus, with the exception that if a player would rather have an apprentice rather than a magus this is technically a companion character, and one apprentice may be created with no magus characters. Companions need not be in the same covenant as the magi, but any player may have up to 2 companions in a single covenant, or any number of "free" companions not attached to a single covenant.
Players may make up to 5 grogs per magus. Grogs may be declared specifically for the player or community property. Players who do not wish to make grogs may bequeath them to other players who have an interest in making them. Grogs when played will be played individually except for turb units which may be brought into the story as a unit by playing one which will serve as the leader of the unit for the story.
Grogs which contribute to covenant finances do not need to be bought as specialists, and there is no limit to how many grogs can be in a single covenant aside from the limits on how many can be made overall. Grogs who develop into significant characters may advance to companions as an exception to the limitation of one companion per magus. Grogs may exist technically independent of a covenant.
Players who make an apprentice character instead of a magus may make one grog as well.
If an apprentice character passes the gauntlet they are considered a magus and the player may make additional characters accordingly.
Regarding mystery cults, initiations, discovering ancient magics and the like- such things are designed to be an in game event, and are not formulaic. If you want your character to have such a background it will need to be discussed with the GM on a case by case basis and depending on a variety of factors (such as what exactly you are seeking and how much it might want you to find it) a number of seasons to accomplish the task will be decided upon by the Storyteller. If you do not want to spend the time to fully gain the sought after advancements partial successes may also be possible. minimum ability scores may also be required.