is it possible to know if a language is regular if its equivalence classes are finite? i have a theoretical questions, and was wondering if you could help me with it so i could understand the material better.

1)suppose we have some language L over $\Sigma$, can we know if L is regular if all of it equivalence classes of relation $R_L$ is finite?

2)and what about L*? is it finite? i mean the cardinality is infinity(alef), but can it be made into a finite language?

Edit: my question is about Myhill–Nerode relation

i am curious about those and your input would really help me understand more about it

thank you very much!
One of the main results of Myhill–Nerode theory is that a language is regular iff its Myhill–Nerode relation has finitely many equivalence classes. You can find a proof in many online resources. In particular, if all equivalence classes of the Myhill–Nerdoe relation of a language are finite, then it must have infinitely many equivalence classes, and so be non-regular.

The language $L^*$ is finite in two cases: if $L = \emptyset$ or if $L = \{\epsilon\}$. In any other case it is infinite.