Appropriate copper pipe length for shutoff valves

As Ryan said you can solder it (either with soft solder or silver solder use flux will make your life easier to) or you can just use a rubber repair on it either buying a propritory type or just making it your self out of a piece of rubber and a couple of hose clamps.

This is a plumb-quik from Fernco

Keep in mind that you don't have to use the whole thing you can cut it open so it is easy to slide over the pipe and put the cut at the top of the copper pipe then put your hose clamps on and tighten it up . I've used this technique to repair a 6" stormwater pipe that was cracked and was a pressurized pipe with no problem.

Another easy way is to use Ferropre or similar a two part epoxy that sets like a rock and sticks to pretty much anything

If you are going to use Ferropre put on disposable gloves, get a bucket of water and mix the two parts together in the water it makes it much easier to handle as it doesn't stick to your gloves as much then once mixed just smear it over the holes in the pipe.

If you can drain the pipe (heating it with water in it is mostly an exercise in futility), then yes, you could try heating it and adding more solder in place. (Which, contrary to your assertion, is not an especially bad idea.)

If not, and you really don't have space to move things, usual practice would be to cut it out and install a "detour" loop -- two L's to bring it out of the plane of the existing pipe, two more L's with a piece of pipe between them to bridge the gap, and two more short pieces of pipe to connect the L's in the old pipe to L's in the new pipe. That gives you the play in the system that you need to bring things together, by letting you make the final connection at right angles to the old pipe. (Of course the downside of this approach is that you have to make eight good soldered connections, not just two, and it costs you a bit more for the extra pipe.)

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