Can't help with the hemp rope but nylon really needs nothing in dry climates. Wet climates they could benefit from take a bar of candle wax and sliding the bar along the rope to coat it. That will help prevent it from soaking up moisture. I wouldn't use any liquid treatment.

Hemp is more susceptible to rot than Manila. Sailors tarred their natural lines but their environment is of course wet.

I have read of Copper Quinolinolate, Copper Napthanate, Tar, Graphite impregnated, and Tallow treatments.

As for recipes, I do not know.

Copper Quinolinolate, Copper Napthanate, Tar, Graphite impregnated, and Tallow treatments.

Where do you get these ingrediants?

Why wait till they break? it's alot easier to replace them before they break Plus rope is cheap. I suggest routinely replace them. real ease with rope still intact. Just remove you front cover. Pull rope out clamp down the spool, cut knot on old rope, remove handle. Measure new rope lenght, install handle, thread through spool winder. tie knot and release holding clamp.

Wait too long and the coil spring could come unwind when the rope breaks. Now, if that happens it's really hard and only a few can fix it on some models.

Better IMO not to wait for disaster.

What is the best type and size of replacement rope to use? Can it be found at Wal-mart, Lowes, etc.?
What to look for in replacement rope? Size-3/16"??? Material-polypropylene, nylon, cotton???

If it's a push mower you can get the rope and handle kit at walmark or any hardware store. For other equipment IMO you need to say with the type that's in the equipment. First pull the rope all the way out. measure it and add 3" or 4". Let it recoil and pull out enough to clamp it. take a sample off the handle end with you to the hardware store.

Different equipment design there recoils to use certain type of rope and may use different thickness and type due to how hard they are to pull.