If i build a mining starbase near a resource say anti matter and its nowhere near one of my planets do i have to build a ship to transport it to one of my planets or does just building the starbase and modules needed automatically add the rss to my manufacturing capability?
Just the starbase and upgrade it with a mining ring.
Also is someting similar needed for Asteroids.
Asteroid mining isn't in yet, the devs have said that it will function the same as with resources.
When i am at the edge of my range with a ship and upgrade my range tech with +10 for example .Should this increas my range or does it just mean i have unlocked a new component that i can build on new ships which will increase range?
Depends. some unlock new components, while others give a bonus.
Can i build a starbase near my borders and will this increase my range?
Yes.