Does a range of have the same meaning as a number of or many?
It will depend on context but generally these do not mean the same thing. the phrase "a range of" is ususally used to indicate variety, whereas the other two phrases indicate quantity.
Example: "We keep a range of televisions in stock" is not the same as "We have a number of this model in stock"
I switched 'televisions' to 'this model' to highlight the different context for an example.
No, because it also implies variation or distinction at the same time. Range is a subset of many, similar to the fact that all ducks are birds, but not all birds are ducks.
For example, an opinion survey is often said to collect a range of opinions. Not only is this many opinions, but it's also many different opinions.
Even in mathematical terms, a range is a group across a set of values.