Heat belt sitting on the bottom is fine provided the door seals are in good condition, and it doesn't get too cold outside, a second heat belt or heat pad can be added if you find it isn't holding temp.
Probe "inside" foam? It needs to be sandwiched between the foam and fermenter.
It's desirable to have a small fan running continuously, typically a computer fan, a few dollars off e-bay, just make sure it's 240v a lot of them are 12v, can be wired into the fridge electrics but electrical knowledge is necessary, a good option is connecting it to the live side of the micro switch that turns the fridge light on and off, get a sparky if in any doubt about what you are doing,
A fridge will soon warm to ambient temp, so no it wont hold 20c if it's 30c outside, one of the reasons people use upright freezers rather than fridges is the insulation is a lot better, but they too will go to ambient over a 24hr period, and don't forget that fermentation produces heat, so an actively fermenting brew in a turned off fridge will actually be hotter than ambient. So yes Tricky needs a working fridge.
Cost to repair a fridge? is a bit like asking how much to repair a car, depends what's wrong with it, blown motor = $1000's, flat tyre = $50.
Fridges aren't really designed to be repaired, if it has a gas leak, probably due to corrosion of the steel pipes (gone are the days they used copper) it's almost impossible, if the compressor has died then it can be replaced but at $400-$500 you're better off just getting another gumtree fridge/freezer.
About the only time it's worth considering a repair is if the thermostat has died, we don't use the fridge thermostat anyway, options are: replace it with an STC1000 ($20) or if using an external controller (inkbird) just short out the fridge thermostat so that the compressor runs when-ever the fridge is plugged in.
There's plenty of you-tube how too's but honestly if you need to look at you-tube to do it, then DON'T! Get a sparky, or a cheaper alternative might be to take it to one of those second hand fridge/washing machine places and ask them to wire it up, it doesn't take long if you know what you're doing, and they're replacing thermostats all the time.