They orbit as stars would in any other halo. It is gravity that causes everything to orbit and "spin around" Stars can also orbit around other stars called a binary orbit.
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The Halo Series
You will need Galactic key and this how to get Galactic key you will need to talk to a Galactic team mate by the Galactic HQ.
In the galactic warehouse to the left of the Galactic HQ
after Halo reach,there is no more In total, there is :Halo 1,Halo 2, Halo 3, Halo ODST, Halo wars and Halo reach
Im not exactly sure what you mean by stars. - In the first Halo: Reach trailer, there were "explosions" by bright outlines that may look like stars. The Explosions are Covenant Antimatter charges exploding or Covenant torpedos (laced plasma with a magentic field). The bright outlines are either the ONI complexs that were destroyed to deny the covenant access, areas already glassed by the covenant, uncovered forerunner structures, or possibly giant military complexs. - In the Halo: Reach World Premiere at the end there were either ONI AA Rockets, escape crafts, ect. If you are talking about the beta im not sure if the stars symbolize anything, sorry if this didn't help much