Is this language is Context-free language or not?
You can't use the pumping lemma to prove that a language is context-free (see, e.g., here).  The pumping lemma is only useful to prove that the language is not context-free.  See our reference questions for details on how to prove that a language is or isn't context-free: How to prove that a language is context-free?, How to prove that a language is not context-free?.

So, one thing wrong with your proof is where you say "if... the word stays inside language the language is context-free" -- that's not correct.