Can I still have my .mac mail messages forwarded to my newer .iCloud account? If so, how?

Your @icloud.com address isn't a separate account, it's simply an additional address to your existing iCloud account. Messages sent to it will arrive in the main inbox alongside messages to your @me.com address without your having to do anything.

The bouncing and the setup in Mail are unrelated. If you are set up for iCloud then all three addresses should receive Mail. What operating system are you using? (Please always post this when you have a question.) If Lion or Mountain Lion you shouldn't try to set it up in Mail: sign out in System Preferences>iCloud then sign back in again. Then enable Mail in the checklist - this should set Mail up properly.

If you are using an earlier system you should follow the procedure appropriate to your system here:

Entering iCloud email settings manually in Snow Leopard or Leopard

Entering iCloud email settings manually in Tiger

As to the bouncing, you will probably have to take this up with Support:

if you currently happen to have AppleCare, either because you recently bought Apple hardware or have paid to extend the inititial period, you can contact them here:

http://www.apple.com/support/icloud/contact/

You will need the serial number of the covered hardware.

If you are not covered by AppleCare, then - in common with other free email services - there is no free support (MobileMe Support is no longer available) and you will probably be asked to pay a fee.