Countries with the Most Tropical Cyclones

Nope. "Tropical cyclone" is a generic term. In the Atlantic and Eastern/Central Pacific they're called hurricanes, and the in the Western Pacific they're called typhoons. Most tropical cyclones form in the northern hemisphere but, as you can see, Australia gets their fair share.

Tornadoes. Yeah, sure. Check yourself before you wreck yourself, buddy.

Why not just say hurricane or typhoon or whatever? It's the same thing. The wind doesn't give 2 hoots whether it's tearing across an ocean English speaking humans call the Pacific or Atlantic. It's a thoroughly pointless exercise in pedantry.

at least from what I've seen, here in the US a tropical cyclone can also be a storm that does not have fast enough winds to be classified as a hurricane

Taiwan isn't that large.

Out of the top 5 countries by area, only 2 show up here. Honestly, I too expected more smaller countries in the Caribbean and the Pacific.

I looked into this and it seems most of the tropical storms and hurricanes approach the Bahamas via north or northwest. Hence, Florida will weaken many hurricanes into tropical storms for the Bahamas. If the quiz included tropical storms with hurricanes then the Bahamas would be almost equal to the US.

The Bahamas do make the "not just since 1970" list (click the source link in the description).

Bermuda is now called a 'British Overseas Territory'.

You may be thinking of monsoons. India occasionally gets hit by a tropical cyclone, but Bangladesh is protected on one side by India and on the other side by Indochina. Most of the severe flooding and torrential rain that you hear about in India and, especially, Bangladesh, are monsoons.

There's a lot of cyclones that hit Bangladesh too though. The infamous Bhola Cyclone in 1970 killed half a million people almost overnight. And even though something that disastrous hasn't happened since, thank goodness, there's still been a lot of cyclones, usually 1-2 per year: https://en.wikipedia.org/wiki/List_of_Bangladesh_tropical_cyclones#Modern_records

source says "However, it should be noted that some basins have longer histories of such activity and this might bias these counts. So the following is the ranking if we only look at storms since 1970, when world-wide satellite coverage became available." tbf

It's shocking how many Americans don't know the difference between a hurricane and a tornado. There was an episode of King of the Hill where there was a tornado and Hank was clinging to a telephone pole. The wind suddenly stopped and Peggy told him to hurry to the shelter because it was the eye of the storm. Um... nope. A hurricane can have an eye that's miles wide. The eye of a tornado, at the point where it touches the ground, would be only a few feet. If you're in the eye of a tornado, you're dead. The writers didn't know that. No one at Fox who reviewed the material knew that. Most of the viewers didn't know that.