What wattage heating element required for 500 degree Celsius oven temperature
1) Both. It depends on how the internal circuitry is driving it, which leads to the answer to the second question

2) That thermostat will drive the heating element on and off in order to achieve the desired temperature. So it will only go up to 250C. You'll need to replace the thermostat (as well as related power cables - they likely won't be capable of handling 15A).

3) There is a fairly complex mathematical relationship between the wattage output and maximum heat. There's no simple way to determine this.

It's also worth mentioning that it may not even be possible to drive your oven to 500C, it's possible that more heat will escape than can be added in a given time unit above a certain temperature.

You will also need to consider all of the other implications of having something at 500C, including things like solder melting.