If Apple Watch is linked on my belt, will it detect fall?

From my experience, the accelerometers and sensors are specially designed for the wrist. You might not get accurate results if you wear it on the belt loop.

It won't work because you need wrist detection on the watch,if the watch can't detect that it's on your wrist then there are many things that won't work.

Don’t like to wear a watch all the time. Can I wear it on a belt loop part of the time ?

You can wear it on a belt loop all of the time but don't expect it to work properly.