Thank you very much. Yes you are right, I was thinking about the verb of existence. Now I know there is actually a difference between the 2.
Forget the second one, when I read your reply I kinda slapped myself LOL, I had confused おいで with まいる...I guess I really need to use more the 敬語 if I do make this errors
My question was due to the fact that いらっしゃい was used with that form which doesn't look like a request or an order. Like saying 読み or 飲み to tell someone please read or please drink...a form I had never seen before.
As per the third question, there was a list of verbs and asked the 謙譲 and 尊敬 of those verbs. They are all the special verbs as in the ones that have a different form (見る、行く、食べる、知る and so on). The last one was 尋ねる so I thought it had a different way to make it humble/honorific. It might be that they wanted as reply うかがう (which I didn't know).