(a) That's right. The essential requirement for a limited partner's limited liability is that they do not take any part in the management of the firm's business. If they do, they immediately become liable as if they were a general partner for any liabilities incurred by the business while they were taking part in its management.
However there are certain things that a limited partner can do that do not count as 'taking part in the management of the business of the firm'. For example, a limited partner can do the following things without losing their limited liability:
Work for the firm as an employee or as an independent contractor
Enforce their rights as limited partners in the firm
Participate in general meetings of all the partners
Inspect the partnership books - Examine and advise on the state of the partnership business.