Does Mobileme check for new mail automatically? If so, can it be set to only check when I click the Send Mail toolbar button?
MobileMe uses "push" technology to send messages to your Mac when they arrive. If you don't want this to happen, uncheck the "Use IDLE command if the server supports it" checkbox in Mail -> Preferences -> Accounts -> your MobileMe account -> Advanced tab. Also, in the General pane of Mail's preferences, make sure the "Check for new messages" pop-up is set to Manually. Then, you just click Get Mail (there's no "Send Mail" toolbar button) to download any new messages.
Can I set a default smtp server when opening a New Message window?
See Mail -> Preferences -> Composing. Look at the "Send new messages from" option.