What do these people do?

Do they get paid?

Why don't they have a competing candidate?

Is post "given" to people who help out the party leaders?

I left them blank, not that it matters. I would be interested in the answers as well.

I can't imagine they are very busy:

DuPage County Regional Board of School Trustees

The Regional Board of School Trustees is an elected board comprised of seven members. This elected board hears petitions for annexations, detachments and changes in school boundaries. The Regional Superintendent acts as Ex-Officio Secretary to the Board. The Regional Office maintains all records of petitions heard in the region. The main responsibilities of the Regional Board of School Trustees are:

The hearing and disposal of petitions for change of school district boundaries.
The hearing and disposal of petitions by school districts to withdraw from Joint Agreements/Cooperatives.
The appointment of appraisers and approval of final settlements in the division of assets when new districts are formed.
Meetings are regularly held the first Monday of each quarter; special meetings are scheduled when needed.

From what I understand they don't seem to do much- mostly maintain teacher certs and stuff. Seems like a wasteful layer of government- sort of like townships in urban counties IMO.