I don't see why it would be weird to write a simple message to someone of the same gender. Depends on what you write of course. Some questions and messages might be aimed specifically at that person (can be male or female), a single gender, or everyone. If you write something creepy then it would probably be weird to either gender. A simple message to the same gender is like talking to your friends of the same gender. Nothing weird about that.
I don't really think so. I've had girls message me just to be friendly, and I don't see a problem with it. I am not on here to find a partner anyway, so anyone is welcome to message me as long as they don't get too carried away.