Methinks the glue/plastic/epoxy/filler/whatever will cost more than a new bowl. The birds won't care what the bowl looks like or is made from, so a cheap one will suffice. Get your wife to choose it: that should score you some brownie points.
Yes, if indeed the entry/fill valve is the culprit. But if the top part of that valve is detachable (the black thing in the pic looks lile a retaining clip?) dismantling and cleaning the valve might do the trick.
Could be the fill valve is passing. Possible culprits are a worn or dirty seal, or (less likely) a leaky float.
Alternatively the flush valve is leaking and the fill valve has to make up for water loss by opening partly.
The flush valve top looks to be detachable near the base for maintenance.
The drum may not be balanced if there is only a small load. If your machine detects imbalance it may well refuse to spin, to prevent excess/damaging vibration.
The 'off' switch on some modern appliances doesn't really turn the appliance off: it merely puts it into a standby (sleep) state. Is this true of any air fryers?
If you like tinkering you could harvest some of those LED chips, using a hot air gun. They're very sensitive and give out a resonable glow at a current of only ~150 microamps.
I'm no expert in this field but (1) I wonder: why would nitrogen be chosen over compressed air for leak detection?
(2) Over a storage period of several years even a microscopic leak could empty the refrigerant, so the soapy water test might not be successful at detecting such a leak.
Sounds like you have a syphon flush with a damaged/worn diaphragm which needs replacing. Perhaps the diaphragm is partially blocking the syphon pipe section above it and restricting the flow?
A relative of mine had nasty side effects from statins, including severe mood swings, all-over body aches and low energy. Great improvement when she discontinued them.
Since your gutters (and your neighbours' gutters) already overhang the public path I'd be surprised if a canopy with a similar overhang would be refused permission. But your visitors could then be subject to drips off the canopy!