When someone trips and falls, is it funnier when they take something down with them?

Definitely.

especially if that something then hits them on their butt as they lay sprawled on the floor
or, even better, if they slip on a banana peel and fall as the banana peel itself flies through the air and lands on their crotchal area

Yes I just cannot stop laughing it was so funny

especially if when they fall it looks like it does in a cartoon as well.

Its equally funny/not funny

Absolutely! For the best effect, it should be a big stack of random objects that make a variety of strange noises, a bell, a rubber duck, an accordion, a whoopee cushion...

Well yeah...as long as it isn't a sharp implement or a bomb.

boy-yoy-yoy-yoy-yoing!