Will this cutter work on synthetic rope, or just natural fiber?

It handles both. The hardened-steel blade cuts synthetic line cleanly — the key is a sharp edge, which this one ships with. Don't let the rope bind in the throat; feed it straight through.

What's the best way to maintain the blade so it stays sharp?

Wipe it dry after use, especially if you've cut wet rope or salt-air exposure. Keep it in a dry space. If it dulls, a sharpening stone or bench grinder will bring it back — it's hardened steel, not disposable.

Can I use this on electrical wire or cable jackets?

Yes, but go slow. The blade will cut through insulation and outer jackets cleanly, but don't force it. If you're cutting live wire, de-energize first — this is a cutting tool, not electrical safety equipment.