No, not all finite languages are regular.
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Yes, according to the theory of formal languages, all finite languages are regular.
Yes, regular languages are finite in nature because they can be described by a finite set of rules or patterns.
No, not all regular languages are context-free. Regular languages are a subset of context-free languages, but there are context-free languages that are not regular.
No, not every finite language is regular.
In general, finite state machines can model regular grammars. Deterministic finite automata can represent deterministic context-free grammars. Non-deterministic finite automata can represent context-free grammars.