Do I need to repair/replace this copper pipe?
the copper pipe is soldered into the valve in the wall and even if it isn't you probably could not unscrew it. replacing it would be a major job even if you have access from the rear. if it leaks some it will be inside the tub area. caulk the hole in the marble good where the pipe goes in, put on the new spout and take a bath.
You do not indicate the sizes of the piping in question, nor what the rating was for the PVC pipe initially installed. This may have some bearing on the method of repair because copper is now very expensive and SCH 40 copper pipe would be both difficult to find and exceptionally expensive if you did. Also, copper is already an extravagant material to use on chilled water piping (not small tubing) when flanged and welded Sch 40 carbon steel is the most commonly used material in larger sizes and screwed galvanized pipe is used for most 2 1/2 and smaller. PCV pipe needs to be supported more frequently than steel pipe and will have a much lower service pressure rating. However, your operating pressure may still be within the allowable range. At these service temperatures, thermal expansion is not going to be a problem regardless of what materials are used. If your ONLY problem is that some joints leak, it is probably because the surfaces were not proplerly prepared and/or the cement was not allowed adequate time to set before the piping was moved around. I would recommend that in this case you forget the copper ( forever) and investigate the cutting-out and proper replacement of the several deffective fittings with CPVC Sch 40, piping and equivalent solvent joint fittings.
Normally I wouldn't advise replacement of the pipe, BUT. best I can tell from the photo, the set screw has penetrated deeply into the Copper, or Brass, pipe, and IF the set screw for the new spout by coincidence hits the exact same spot, then it could cause a leak. In that location, and with caulking around the tail of the spout, it could continue to leak without your being able to observe it. That could result in severe water damage to the structure behind the tub enclosure. I can't tell from the photo whether that pipe is a threaded nipple, or a soldered-in nipple. If it's threaded, then removal and replacement is pretty simple, BUT. if its soldered into an ell or a tee behind the tub enclosure, then that will mean opening up the other side of the wall to replace the pipe. Another fix I would use would be to clean the damaged area well, and fill it with a two-part epoxy product called J-B Weld, made in Sulfur Springs, Texas, and available at most auto parts stores, and many local hardware stores nationwide. This could save a lot of work replacing the pipe, although that is the best thing to do.
