Are they doing their own business out there or doing contract work for NASA or with SpaceX?
Could anyone elaborate?

They are doing contract work for NASA.

Thanks, but was hoping for more insight as to which projects and for how long.

Also, does anyone know if that new rocket works, would they end up having to go through NASA for any official launches related to the moon or mars?

Jacobs has the Test Operations and Support Contract (TOSC) which encompasses support for the International Space Station (ISS), Ground Systems Development and Operations (GSDO), the Space Launch System (SLS), Orion Multi-Purpose Crew Vehicle (MPCV) and Launch Services Programs.
ETA
Jacobs will be assembling NASA's SLS launch vehicle they don't have their own ship, they are a NASA contractor. In simple terms kind like United Space Alliance was with the shuttle program.