If Celestial bodies have increasing expension recession velocity would their mass increase also acccordingly?

Answer 1

From our point of view, yes. Of course from the point of view of those distant bodies, it is we and not they that are moving away at increasing velocity and gaining mass. Everything in relativity is relative.

Answer 2

Not at all. It is just the space which is expanding. The structures like starts, planets, galaxies, etc. are not moving as are objects in our ordinary space, so we cannot apply to them the ordinary laws of mechanics, were they classical (newtonian) or relativistic (special relativity).

Structures subject to cohesive forces, such as electromagnetic (tables, chairs, planets) or gravitational ones (planets, stars, galaxies, even galaxy clusters) do not participate of the space expansion. Celestial objects need to be far away enough to recess due to the space expansion.

Due to that reason the redshift of the recessing galaxies is not considered a "Doppler redshift". It is called "Cosmological redshift" instead.

It should be taken into account that special relativity does not apply to large scale univers phenomena. Special relativity applies to reference systems moving with uniform speed. Universe large scale phenomena needs general relativity. That explains why we can receive light from sources that are receding from us at speed larger than the speed of light.

I apologize for my poor English, but I hope I made me understood.