they are all technically grammatically correct, but the third is the most natural and most commonly-used in english. the first is very formal and would only be used in a formal setting, not in daily conversation. the second is grammatically correct, but it has a different meaning. "a thunderstorm can happen tomorrow" doesn't tell the listener that you are trying to predict the weather, it just sounds like you are listing all of the possibilities. great job and keep up the good work!!!

Shuuuuuuuu! I agree with Phil's answer, but I will add another option. We sometimes use the verb "to have" with some kinds of weather. For example: "We might have a thunderstorm tomorrow." or "They might have a snowstorm tonight." Good luck!

We don’t use can in predictions. Only could, might, may

These are all grammatically correct, but #1 contains a redundancy, and #2 is unnatural. #3 is the best of the three. Alternatives are, "There is a chance of a thunderstorm tomorrow," "Thunderstorms are possible tomorrow," "A chance of thunderstorms is in the forecast for tomorrow," or "There is a possibility of a thunderstorm tomorrow."

Believe it or not, they’re all grammatically correct, but I wouldn’t say any of them. For one thing, we wouldn’t talk about a thunderstorm “happening”, for another, we wouldn’t normally use “can” to speculate about tomorrow’s weather. “Could” would work, but I’d normally use “might”. “There might be a thunderstorm tomorrow”, or “There is a possibility / chance of thunderstorms tomorrow”.