If I buy a premium membership, does it extend to my group or does each one of us have to pay?
Todoist Premium applies to a single account so your colleagues will not get Premium accounts when you buy one.
Please note that collaboration/project sharing itself is not a Premium feature so not everyone needs to have a Premium account to share projects.
So if I create a task in a project that is shared and I put an alarm, note or label on it, will my partner see it if he does not have a premium account?
They will need Premium to get reminders, they will get notified about a task you assigned to them though.
Do you at least have a family plan pricing. $120/yr for a family of 4 doesn't go over will with the money manager of the family.
Unfortunately, we don't offer such discounts, but please note that sharing itself is not a Premium feature so with the exception of reminders (which are Premium), you could share projects with your family, assign tasks to them, set dates and times and post comments on tasks.