I dont want a @me.com

If you are talking about creating an Apple ID, you can use your own e-mail address to do that. If you are talking about the free address you get with your account, simply set it up and don't use it.

iCloud will only support me.com/mac.com email accounts, not those of third parties, such as your professional domain name. For that you have to define an email account in the mail app for your domain. It has nothing to do with iCloud.

Don't know what you mean. As others have suggested, your issue has nothing to do with iCloud. Just set up your email account on your iPad in the normal way through Settings>Mail, contacts, etc., and then you will achieve what you want, i.e. syncing of your mail and notes.

iCloud will only synchronise an iCloud mail account across devices. If you want to use your own mail account then you need to add it to both devices manually as suggested above.

That can only happen if your professional domain provider has IMAP email included in your plan. If it's POP only, then you don't get syncing capabilities. As we've said, this has nothing to do with iCloud and everything to do with your provider.