Mail program delays, search issues, and non-responsiveness with Gmail and Exchange accounts

Having all sorts of issues with Mail. Outgoing messages not sent immediately. Takes 30-90 seconds for it to be sent. The search feature doesn't reveal previous messages or addresses in my Mail folders. I get the "twirly" symbol which often won't go away, and Force Quit shows Mail is not responding. I have a gmail and Exchange account in my Mail program.

[Re-Titled by Moderator]

Original Title: Mail program