I've been solving a lot of questions lately about determining the type of a given language, by type I mean whether it's regular, CFL, in P, Turing-decidable, Turing-acceptable, or all the languages. and I have this language here: $$L=\{w:|w|\text{ is even, and it has }\frac{|w|}2\text{ consecutive 0's}\}$$ So my main purpose is not actually to know the type of this language but I've faced a lot of questions that asked in the same manner, meaning it asks if the given language has a substring with some characteristics in the first half of a string $w$ in the language or such a thing as appears above.
So I'm searching for an approach that I can adopt to solve such questions.
Also, I would like an answer for the type of the above language.
I assume the language to be CFL but don't really know how to build finite automaton or CFG to decide it, it's clear that it's in P but I'm willing to know if it's CFL or regular.