Our bin lid behaves much the same way. Also, it's cunningly designed so that lifting the lid to tip off the water results in water entering the bin via the hinge section!
The size and weight of the flag will determine the best type of fixings to use. Also, is the flag likely to be exposed to high winds? Do the fastenings need to be removable?
Looks to me as though the driveway has sunk slightly at one point, causing the track to sink likewise. Can you prise the track up slightly and insert some packing below it at the critical point?
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.