It's possible to use a separate SMTP server, but the email accounts for members won't work. This won't prevent anything from function (like notifications), just they will no longer have their own email account.
GMail, Yahoo, and many other ESP's often do not show images in an email unless a person clicks a link saying it's ok to show the images. If they don't click that link and images are never shown within the email then it will not track the message as being opened. Also, if the email is not an html email it will not track the message being opened.
To handle spam we charge email overages and use that to determine a sites usage instead of bandwidth or other methods.
Our email delivery is not perfect. It is typically better than others because we charge for emails,
plus good enough where you can largely develope YOUR OWN reputation with negative impact from us (a more neutral launching pad).
Also, if a bigger issue, we offer dedicated servers with dedicated IPs that we manage NOTE: Additional setup fee's will apply.
Then, you can do a wide range of additional things (like purchasing certification, 100% own reputation, etc).