Plumbing – How to plumb an outside line to a roof deck faucet

Yes. In fact, I had to do this exact same thing in a house in MN that had baseboard copper freeze and burst in an attic. I ended up replacing the cooper between the boiler and the baseboards with PEX.

I'd suggest using SharkBite connectors to transition between the copper and PEX. They're designed for that and it's super-easy to install.

As Ecnerwal points out, be sure to use PEX with an Oxygen Barrier.

While doing this, be sure to fully insulate the PEX. PEX can withstand freezing, but it's best to avoid freezing in the first place. If you can move it into conditioned space, that'd be best. If not, wrap it in quality pipe insulation (not the cheap stuff but the ones that self-seal).

The biggest challenge might be finding just the small amount of PEX needed as they are often sold in large rolls. You may want to check with a plumbing supply warehouse to see if they'll sell you a remnant piece.

I would not double back. I would consult your heat tape/cable directions. If you no longer have the directions, I would google the make/model of your heat tape/cable to see what the manufacturer recommends when it is too long for what you need.

In general, if it has a plastic piece at the end (as the one I used did), I would not cut it. If you can't cut it, just put it a little longer and use a small electrical cord staple to affix it to the joist beyond the pipe.

It should be perfectly safe to put the tape/cable next to wood, most of these heat tapes/cable are designed to keep the temperature just above freezing, and are self-regulating to prevent them from getting too hot (as long as you don't cut them when they shouldn't be cut :-). I would definitely do a little research to get the manufacturer recommendations.