I would disconnect the battery, remove the protective sheath, and make sure that's the only section with missing (or compromised) insulation. Something caused that - maybe a fluid leak - and you need to be sure of the full nature of the problem before creating a solution. If anything touched that battery cable, you could fry every electrical component or even start a fire.
If it's really just that section, you have a few options for repair. The cheapest option would be heat shrink tape - although I'm not sure there is such a thing as auto fluid resistant tape. After that, you're into specialized tools so you might be better off just ordering a new battery cable.
Is it heavy duty? There's a LOT of amps available out of an auto battery.
I don't think coolant would eat plastic. Seems unlikely given the use of the product. But anything in the auto area should be oil/gas/etc resistant anyway. Are you in a hot climate and it's just heat /age fatigue then a little mechanical motion when you were working on the car?
I would think so. A decade ago I had to buy one for my dad's 9-3 and that was about the price.
I could build one for less, but probably not enough less to justify the hassle.
Bob: I agree - it's not coolant. That's power steering or brake fluid, or maybe some foreign chemical.
OP: The problem with heat shrink TUBE is that you need to get a size for the cable, and it won't slip over the battery terminal end. If you're comfortable physically removing the cable at the starter/alternator end, then totally, heat shrink tube is a valid way to go. You can buy tube rated for the job from remybattery.com … be careful with no-name/Amazon/ebay options as you just can't guarantee quality. FWIW, Harbor Freight sells a MARINE GRADE pack that is quite substantial and I've used successfully for years. I would personally use only adhesive-lined tube ("marine grade") to ensure the repair doesn't let moisture in.