[RadioKid]

question 1:
You can understand "~しておく" like as " ... and leave it".
"私の親に電話をして置きました" would be "I have called my parents and left everything to them".

question 2:
It is difficult question even for native Japanese to answer.

After some study, I found it is to diny other's opinion very very politely.
Becuase ありがとうございます is "you are so kind or generous that it is rare or no one can expect it" word by word, denying ありがとうございます can be a polite answer for it.

As my personal opinion, どういたしまして could be "how can (I)?"."how come!?" or just simply "why?".
Adding some other words like as "受け入れられましょうか", it would be "how can I accept it?!".
Do you accept these?