can static electricity travel through space ?

i dont think so.
because electricity either static or dynamic it needs some coductors to transfor of electrons. in space there is no coductor.

no
it is not in motion
hence the name "static" which means stationary

Yes.

Even space is not COMPLETELY empty.

The Sun constantly emits streams of ions, charged both positively and negatively.

When you have a surface that these ions contact, a static charge can build up.

It's the transfer of electrons to the charging object that builds the charge.

even in space there are tiny particles that could cause say you finger to build up a charge after a very long time. i suppose the space suit could be a problem.

basically if you can build up a charge then it would still travel through space.

Static electricity CAN travel through space but only if there is an existing electric potential between two objects. Electricity only "travels" when there is a path that the electricity can follow, and a path consists of electrically conducting materials. In space if you put two metal orbs in space and charged one of the orbs using static electricity then the electricity would "travel" from the charged orb to the uncharged if the two orbs were close enough to each other.