The tank is still running for now although we understand the filter bacteria will die off without any fish in there now.
No, this is not necessarily the case. It does however depend upon the "issue" and how it was treated, as some preparations (antibiotics especially, but others too) will or can kill bacteria (obviously) including the good ones. Normally, thee nitrifying bacteria will go into a sort of dormant state, for anywhere from days to weeks, depending again upon the specifics of the system. The longer the bacteria is "in limbo," the longer it will take to re-activate. Drying out will kill it, as would extreme temperatures. I just wanted to point this out, so we can now move on to your questions.
What can be safely disinfected and kept? We have gravel, live plants, a rock, and a chunk of mopani wood. The filter is sponge and ceramic rings.
It would depend upon thee issue, which we do not know, so I will respond with the safest method. Never use wood, and usually not rock either, as these (wood especially) will absorb substances in the water and they may leech out days, weeks, even months later. There is no way of boiling or baking to eliminate this, depending what it is. Same for any filter media; ceramic rings could be boiled and should bee safe, but certainly not any sponge/floss/foam media, or any biological media which is extremely porous to provide a lot of surface area for bacteria to colonize and disinfecting this is next to impossible. Here again any preparations used initially or in an attempt to disinfect now, will be absorbed and leech out. Gravel I would discard, same reason...porous substances can hold all sorts of things. You can get a bag of play sand, if you want the most inexpensive substrate and one that is ideal and safe. The plants should be safe; do not use any substance on them--anything effective enough at killing whatever will harm the plants. The tank itself can be cleaned (after being totally emptied) with a solution of bleach and water, then rinsed a couple times very well, then allowed to completely air dry. Same with the filter housing and heater.
This might be a really stupid question but I'll ask anyway - is there any way we could we keep the tank set up? For example is there anything we can add to the water to disinfect the tank with, without harming the plants, or can we just wait for a few weeks to allow whatever this mystery thing was to die off/expire etc? Or are there aquatic nasties that can keep going without fish?
Not stupid at all. Unfortunately without knowing what the issue was, this could bee very risky. If the problem was ich for example, leaving the tank running for two weeks at a higher temperature (86F/30C) without any fish would deal with ich as it needs a host plus the warm temperature will kill it. The plants might weaken but should recover, except perhaps very delicate species.
Using any "treatment preparation" is not advisable because without knowing the issue this is hit and miss, and the substance may enter the substrate, wood, filter media and cause more trouble anyway. Same for the wait period; some bacteria (good or bad) can live for long periods as I mentioned above, and so might other living critters depending what they are.
