Is there any possibility that on other planets there can be earthquakes and other natural disasters?

Yes, Absolutely

Explanation:

There exists a possibility that other planets on our solar system have various natural hazards like situations as the case of Jupiter, Mars and Mercury and Neptune. Sun being a star also faces lots of storms. These storms may be magnetic in nature or geologic in nature. Like the Jupiter red-eye or jovian spot, which is a persistent anticyclonic storm going on for centuries. Likewise, mars have lots of dust storms, which can lead to an electric atmosphere, mars also have large martian mountain and the presence of cold polar type caps. And the planet mercury is considered to have an earthquake just like earth because of the active tectonic processes that shape the landscape.