Welcome to the forum!
It sounds like the bulb/lamp is going fast. Was the TV on when the power went out? Lamps need the fan to blow over it to cool it down and if the power went out while it is on it did not cool down properly. This is why you should have it plugged into a UPS.
As far as how to know what resolution the signal being fed to the tv is, you should look for an "INFO" button. That should do it.
Good luck!