A grammar is ambiguous if we can drive a string in the language with two different derivation steps.
A language L is called an unambiguous language if there exists an unambiguous grammar that generates L.
If every grammar that generates L is ambiguous, then the language is called inherently ambiguous.
Now,
Regular Languages: Yes there may exist an ambiguous grammar. But that doesn't mean that the language becomes ambiguous.
For regular language L, we always have a regular grammar that generates L and it is not ambiguous.
For ex: S $\rightarrow$ aA / ab
A $\rightarrow$ b.
In this, we can generate the string 'ab' with two different derivation steps. So this grammar is ambiguous. But if can find a different regular grammar that generates the same language L and which is not ambiguous. For Ex: S $\rightarrow$ ab.
To prove that Regular languages can't be ambiguous we can have a different argument.
For every regular language there exist a DFA and in DFA every step is well determined. To generate a particular string we always have definite steps. So we can't have two ways to generate the string.
DCFL: For DCFL we have deterministic PDA, Where for a particular string we have well-defined steps to generate it. So they are also unambiguous languages.
CFL: Context free languages may be ambiguous or unambiguous.
Actually, inherent ambiguity begins from this layer. Therefore upcoming layer can be both ambiguous or unambiguous.
Hence, CSL, Recursive languages, and Recursive enumerable languages may be ambiguous or unambiguous.
