is it true that very small dogs are extremely fragile and can even break a leg jumping down from a bed or a chair?

Yes, many small dogs are known to be somewhat fragile. This applies to breeds such as Chihuahuas and Yorkshire terriers. It's better to prevent them from jumping down from relatively high for their size spots.

Of course they are. Virtually every young being is fragile, including toddlers.
I think that is sad because they can break just by jumping from a chair or bed it is sad