Some pipe welders work in fabrication shops. Some work on specific construction sites and others work on pipelines.
Those in shops tend to do most of their welding with the pipe in the horizontal position but some with the pipe in the vertical position. Also as much of the welding as possible is done with the pipe being rolled so you are doing the welding in essentially what is a flat position.
Construction site welders have to be able to weld in all positions because they are typically making tie in welds to pipe spools that were fabricated elsewhere. They are usually tested in the 2g and 6g position.
Pipeline welder almost always weld with the pipe in the horizontal or bell hole position..
In addition to welding just pipe the pipe welder also welds fitting and sometimes valves to the pipe. As to repairs that varies with the company or job. Some jobs require the welder who first welded the pipe to repair his own welds. Other use the repair process to break in new welders.