anglophile: Dating your brother? Let's not get ridiculous shall we. But then again, if your brother said "Hey sis, let's go see a film Friday night" and you reply joking "It's a date". Then Yes, you're dating your brother.
You have a dictionary...then use it and look up the definition. If not, then let me help you out.
Date, (noun)
An appointment, especially an engagement to go out socially with a member of the opposite sex, for example.
The American Heritage® Dictionary of the English Language, Third Edition copyright © 1992 by Houghton Mifflin Company.
If a guy says "Will you be my girlfriend?" and you say "Yes" then a decision has been made and you are now in an exclusive relationship.
On the other hand, if he decides he only wants to see you but you prefer to see other people at the same time then there is not a mutual feeling thus no relationship.
No, I wouldn't say my vision is narrow.
Your idea of dating someone seems to be very different from my experience here in the UK, maybe its a cultural thing

, but for me if I am "Seeing" someone, but not yet in a relationship, I would still be exclusive to that person, how else can you build up to it becoming a relationship, I would feel that the person I was with was not particularly interested in me, its as though I was just a convenience, just there when others where not available.
Surely you would know within a very few meetings if you were attracted to the other person and if the feelings were mutual you move forward.
I had no idea that saying "will you be my girlfriend" was still in vogue, last time I said that I was about 10
No offence intended, just teasing ok