If electron charges are constant Than as they move at high speed(relativistic) would they lose mass in space??

Answer 1

Mass has nothing to do with electric charge. For an electron travelling through space at any speed, it will only lose mass (or energy, this is equivalent) if it loses energy by interacting with radiation or with matter (other molecules in space, there are several of them per cubic meter even in what we call the interestellar vacuum).
For instance, if an electron finds a dust cloud in its trajectory, chances are that it will impact with some molecules, losing energy and therefore mass (Einstein equivalence E=m x c^2).

But an electron can lose movement mass. Its mass when it does not move with respect to a reference system is also constant.

Answer 2

They can't move faster than they move without a reason, such as being sucked towards a black hole, as such they don't lose mass. If anything they slow and gain mass.

Answer 3

no

Answer 4

No.