Is Equality problem decidable in DCFL and CFL?
We can't. Infinitely many different PDAs for the same DCFL exist.

In 1997, Géraud Sénizergues proved that equivalence of DCFLs is decidable, and he was awarded the Gödel Prize for it.

For general context-free languages, it is undecidable.
As a matter of fact, it is already undecidable for linear context-free languages.