It is true that the phone polls for emails rather than having them pushed to you (although I would guess you could sign up to a service to provide this function at a cost). I personally am happy with my mails being buffered as this makes me less of a slave to them. But you can adjust the polling frequency if you don't mind running your battery down faster. You will find this option by opening the mail client, opening one of your inboxes and clicking the options soft button. Then go to more-> account settings. In there you will see the option email check frequency. You can select a different time and your emails will arrive faster.
Also, I use keyPassDroid to store my passwords encrypted. Seems to work fine (better than my memory in any case).
Hope this helps.
Regards,
Eric.