Can I use a non "me.com" address to send email with iCloud?

Using iCloud doesn't necessarily means you'll have to use Mail on iCloud. You can still use your current mail provider to send/receive email on your iPad. Providing you can connect to your current provider using IMAP, Exchange or POP.

You can also create your iCloud account without having a @me.com address. I use my @gmail.com address as my Apple ID to connect to iCloud to sync Contacts, Calendars, etc.

If you use iCloud mail, then you can not use any other email address than me.com. You can forward the mails from your old email to the me.com, but if you send an email from iCloud then the sender will be me.com. This is a serious issue with iCloud, and I personally hate it.