Is there any relationship between grammar being ambiguous and the language itself? According to my understanding, a grammar is ambiguous if it generate strings which can be interpreted in more than one ways ( that is , more than one parse tree), but when it comes to the language itself , is there any kind of relationship between the language itself and the ambiguous nature of a particular grammar that could generate it. Also , I am having another doubt , Is it possible that there should exist,infinite number of grammars that could generate the strings of a particular language ?
There exist context-free languages which have no unambiguous grammar. Such languages are called "inherently ambiguous".

On the other hand, there is no such thing as a language which does not have an ambiguous grammar; any grammar can be made ambiguous by duplicating some or all of the non-terminals.

The fact that inherently ambiguous languages exist is interesting, but they rarely if ever show up in real-life parsing problems.