Opt not to leave messages on the server (unless you're using recent mode to download mail to multiple clients). This does not affect how Google handles your mail. That is determined by the POP settings above.
If your mail client does not support SMTP4 authentication, you won't be able to send mail through your client using your gmail address.
If you're having trouble sending mail and encryption is on for SMTP for your mail client, configure your SMTP server on port 465.