What should I write in that area?
For the references you are putting down, how would you categorize the relationship: Is this person your manager, team lead, teammate, subordinate, or something else? Where in the organizational chart are you in relation to the reference. Was this person a client of yours? Did you use this person as a vendor for some service? There are more than a few possible answers here.
Also, when I report to a person who is the only other person in the
company, what is their position: owner/manager/MD/CEO?
This can vary. President, CEO, Owner, Founder, Creator, and Chairman are possibilities though it depends a bit on how the person views the company. They may just see themselves as a Principal or Director and thus it is worth either asking or looking at their business card or an on-line profile like LinkedIn that may have their title.