1. 〜き is the classical form of the 連体形 of 形容詞. Sound changes caused き to turn into い for the modern 連体形 (and 終止形).
2. 〜き works exactly like 〜い in modern Japanese, except it can't be at the end of sentences, it can only be in relative clauses: ○高き壁、ｘ壁は高き
3. No, any 形容詞 can end with 〜き in classical (or pseudo-classical) Japanese.
4. いと is also old (いとも being the only related word used in modern Japanese), so it'd be unlikely to see it mixed with an 〜い ending, but honestly there are no rules for creating pseudo-classical Japanese text, so someone could decide to use いと with 〜い if they felt that it gave the right feel to their text.

I would certainly not recommend using either the 〜き ending or いと yourself.

1. 〜き is the classical form of the 連体形 of 形容詞. Sound changes caused き to turn into い for the modern 連体形 (and 終止形).
2. 〜き works exactly like 〜い in modern Japanese, except it can't be at the end of sentences, it can only be in relative clauses: ○高き壁、ｘ壁は高き
3. No, any 形容詞 can end with 〜き in classical (or pseudo-classical) Japanese.
4. いと is:

• an adverb (副詞), not a prefix -- it can modify any adjective (in any conjugation) and any verb
• archaic (いとも being the closest word used in modern Japanese), so it'd be unlikely to see it mixed with an 〜い ending (as opposed to classical endings 〜き, 〜し, etc.), but honestly there are no rules for creating pseudo-classical Japanese text, so someone could decide to use いと with 〜い if they felt that it gave the right feel to their text.

I would certainly not recommend using either the 〜き ending or いと yourself.