I don't go near Exchange. However, I use my gmail, hotmail and iCloud on my iMac and iPhone.
I input hotmail under Google since it's one of theirs. I did the same with my gmail.
I ran connection doctor on my iMac after to test incoming & outgoing servers. One didn't want to initiate but with the help of this nifty lil' tool, it pulled through quite easily.
Also, you've probably referenced the following, but I'll post in case you haven't & may want to take a look at (The second one I feel is a wise move - updating your password may help, but I have a feeling a big part of it is network related also. However, updating a password can't hurt...if nothing else and I'm sure as you know, it's smart to change it fairly often anyhow):
Mail may say that it can't connect to your email account, and repeatedly ask you to enter the password for it.
Mail is connecting to your email service provider, but it can't connect your email account because your email provider isn't accepting your email password.
Your email provider may reject your password for several reasons, including:
- You're not using your current email password. If you updated the password on another device, make sure that you're using the same password on this device.
- Your email provider needs you to update or reset your password for security reasons. For example, if you turned on Google’s two-step verification, your Gmail account in Mail now requires the appropriate app password.
- Your email provider deactivated or suspended your account. Contact your email provider for help.