Is there a way a proving a language regular/non-regular that works for every possible language?
No, there isn't. It is undecidable, even for context-free languages. It is decidable for deterministic context-free languages.

References are easy to find with Google; for instance,


Undecidable Problems for Context-free Grammars, by Hendrik Jan Hoogeboom
Deciding whether a context-free language is regular [closed], on the Theoretical Computer Science Stack Exchange, in which user babou lists


A regularity test for pushdown machines,  R.E. Stearns, Information and Control, 1967 (full text by clicking on the page)
Regularity and Related Problems for Deterministic Pushdown Automata, Leslie G. Valiant, JACM 1975