Say for example, I have The Board rezzed, and the runner has stolen some copies of Domestic Sleepers, are they each now worth -1 agenda point?

Also, does The Board affect cards that act like agendas once stolen, such as Chairman Hiro, Director Haas, and funnily enough, The Board itself?

First question I'm unsure of, but I assume yes (Shi Kyu can give negative points, so why not?)

Second question, I'd also say yes. They are added to the score pile as an agenda. Philotic Entanglement treats them as real agendas, so one assumes the board does too.

I'm almost certain that the board would work on all agendas including domestic sleepers, and all other cards that can be in the runners score area. The board, director haas, chairman hiro, shi.kyu, and notoriety would be affected too as they each refer to themselves as agendas when in the runners score area. That's my take anyway.