Islander

This site has pickguard material: https://www.axetec.co.uk/guitar_parts_uk_021.htm

Yes but there's a difference between a good mechanical contact and a good electrical one. The first is just a matter of doing everything up tight enough, the second means that you have to ensure that contact areas are both clean and tight. It's possible and acceptable to use the control plate as an earth path rather than having the additional wiring, but it does mean you have to ensure that good electrical contact is made between the pots and jack and the control plate. Using a loop of wire soldered to the back of each pot and to the earth tag of the jack is generally more reliable in the long term as long as good solder joints are made.

I'll just add that that's the way I'd expect it to be wired - it removes the dependency on good contact with the control plate

Yes, the control plate

It looks like the metal plate is being used as an earth conductor which is fine as long as all of the fittings are tight and making a good connection.

Any electronic equipment can fail and any electronic equipment can be repaired by somebody who knows what they're doing. Whether it's worth it or not is another matter entirely and that's simply down to the cost of a replacement against the cost of a repair.

I usually spray a good amount into the opening in the pot cover by the pcb contacts/wiring tags and work the spindle back and forth quickly a few times. That's usually enough to clean the track and wiper. If that's not working after a couple of applications then I'd replace the pot. Volume pots are usually logarithmic (log) rather than linear (lin) so make sure you check the markings to ascertain this as well as the actual value before you source a replacement.

Yep, I suggested it as a stopgap while the OP arranges to replace the old pot. It'll help settle and distribute excessive particulate buildup but if the carbon track is that badly worn then it'll have no effect.

You could try a small drop of light oil but it'll probably just be a stopgap. Replacement is the best option.

There's a third fuseholder under the two red wires at the top left that should hold a 250mAT fuse, the other two hold 2.5AT fuses. All are standard 20mm. It looks like a simple enough job to replace the broken fuseholders. The PCB will have to come at least partly out to gain access to the underside but that shouldn't be too difficult. There's a service manual here that you might find useful... https://elektrotanya.com/warwick_hdb-electronic_tube-path_5.1_sch.pdf/download.html