Would a light bulb be brighter if there is more power available. At different times power companies have more power available. Is this why all our globes blow at the same time and the fridge blows up?

A conventional bulb (non-fluorescent) will be brighter if the voltage is increased - not necessarily if more power is available.

Power companies in most countries have requirements about the range of voltages that they are allowed to provide to consumers. For example, in the USA power companies try and keep the voltage supplied between 114 and 126 V. Suppliers of electrical equipment design their products to work with (at least) this range.

Whether unusually high voltage is affecting your bulbs and fridge is difficult to say.