Hello,
This is (your name), (older brothers name)’s sibling. My brother has recently been accepted into a great university and my parents are throwing a surprise party to celebrate. You are invited to join us celebrating during (date of party). Make sure not to mention this to them as it is a surprise party.
Sincerely,
(Your name)
The answer is all of the above except choice 3.
In a business setting, you never want to use a detached tone. This gives the impression to your colleague/boss/etc. that you don't care and don't really want to be there. It shows that you don't see them as important and don't care about what they have to say. It won't achieve anything for you.
Gatsby is nervous about meeting Daisy at Nick's place. He is panicking and Nick tells him to stop acting like a little boy.
