grammar - Adjectives and particles が に

Adjectives describe a noun which is marked by が.

僕は料理が得意。

Could it be rewritten as

僕には料理が得意。

Or is it wrong?

Regarding adjectives, a sentence like this would be correct:

僕にはペンが必要です。

Would a sentence like the following one be correct?

僕がペンを必要する。

(I think I should say 必要にする, but I am not sure.)

Answer

僕には料理が得意。

is simply ungrammatical.

僕にはペンが必要です。

is grammatical only because 必要だ can take two arguments (AがBに) as word-specific feature, not that it's a universal grammar for adjectives. It's like the English word worth can have an object but most other adjectives can't.

Other adjectives that take に include ふさわしい (あなたが隊長にふさわしい) and 夢中だ (僕は君に夢中だ) etc., but basically you have to learn one by one.

And as already pointed out in comments above:

× 僕がペンを必要する。

僕がペンを必要にする。 → I make the pens necessary.
僕がペンを必要とする。 → I necessiate a pen.

na-adjective + にする results in a verb "make ... adjective" and とする "regard ... adjective".