Taking an oath on anyone besides Allah Ta'ala

Q: I just came to know yesterday that taking a qasam of ghairullah (anyone besides Allah) is not allowed in Islam.

I don't remember taking a qasam of ghairullah but I have a doubt that years ago I might have asked someone in texting to take a qasam of his mother and he refused to take it. I was ignorant about it. What should I do now?

Is asking someone to take qasam of his mother is also sin? although he refused to take it. 

Hajj-e-badal

Q: I am looking for a good source for Haj-e-Badal. I have performed my Haj and have wish to perform Haj for my dad who is no more. I will be doing it with my money, so I believe I can do Haj-e-Tamattu also. Please correct me if I am wrong.

Fasting on Mondays

Q: Is there any truth to the claims that Nabi (sallallahu alaihi wasallam) fasted on Monday because he was born on a Monday. If it is true, is it permissible to use this to say that one can celebrate his birthday?