Can the antenna on a T5820 be replaced?

I believe for the FR60 walkie-talkies, if they are not sending or receiving, the issue could be related to the antenna, battery, or internal components. You can try replacing the batteries and/or antennas to see if that resolves the issue.

As for the T5820 walkie-talkie, if the rubber on the antenna is broken, it's likely that the antenna itself is also damaged. In this case, you can try replacing the antenna with a new one. Antennas are typically available for purchase online or at electronics stores.
In terms of cost, repairing older walkie-talkies like these may not always be cost-effective. If the repairs are extensive or require replacement of major components, it may be more practical to purchase new walkie-talkies instead.
Below are options of the options of walkie-talkies you can buy;

The power cord should be a standard 3 wire cord. Any hardware store. Just buy the length you want. You will have to remove some covers/plastics to get to where the cord connects inside the vacuum. Look for screws holding panels in place. Once inside, you'll see how the cord is attached. Just replace the old with the new. Not critical which of the flat prong wires goes to + and - but be sure the ground wire (usually copper) goes to the ground screw and not a hot connection.

shorting the wires usually just blows the fuse on the control board in the inside unit. BUT there is a chance the contactor coil was shorted out as well. Will the inside fan come on if placed in the ON position but the system switch in OFF ? If not check the transformer in the cabinet of inside unit.

Either you have blown the low voltage fuse located inside the air handler (if there is one) or you have blown the transformer feeding the low voltage control wiring.

If the transformer is blown due to no fuse installed, I would recommend installing a low voltage 3A fuse in line with the red terminal coming off the transformer. This will protect the transformer in the future.

Same color to same color.

the hanes jeep manual located at any autoparts store for this model cherokee comes complete with full detailed wiring diagrams, if you're lucky you can find one cheaper on amazon or ebay but they're very usefull for small repairs and troubleshooting!

You can cut the bad section of wire out of the cord, cut the insulation on the cord to get to the wires. Match your colors, strip the insulation from the individual wires and twist together. Wrap each wire with electrical tape (making sure no wire is exposed, can be a fire hazard), then wrap the cord with electrical tape. The cord will be a little shorter, but should work fine.

If the dog chewed up the coil wire you will need a new coil. How did the dog GET to the wiring? Did you let the dog live? The wires are color coded. Splice the wires color to color. Depending on how badly the dog tore up the wires, you may want to get a new, (or used) wiring harness and re-wire the bike following the pattern of the existing wiring.

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First : Teach the dog not chewing wires or everything usefull.
Second : replace the wire.