Is it safe to give out your Apple ID

If someone knows your Apple ID and password, they will have access to the same personal content as you do. eMail, messages, contacts, etc. I certainly would never share that type of info.

Why would you even do that? You're giving that person 50% of what they need to know to access your account. There are billions, if not trillions of possible email address names to try and guess, and you will have narrowed it down to one. From there, it's just a matter of guessing, or finding out your password.

There is very little, to no justification to giving anyone else that information.

Is it unsafe to give out your Apple ID only? Not password.

No. There is no legitimate reason for anyone outside of Apple to know your Apple ID.

Isn’t your ID compromised then each time you send an email from your icloud email address?

Knowledge of an email account is not an issue, though I'd not advertise that a particular email account is also being used as an Apple ID, or as a backup for an Apple ID.

In some cases—such as with iCloud email accounts—that there's probably an associated Apple ID of some sort is clear. (iCloud does allow a couple of email alias addresses, though.)

Knowledge that an email address is being used as an Apple ID means that folks might try to obtain your password by sending fake email tempting you into clicking on a link in the mail leading to a password change form created to look like one at Apple, for instance.

Or the folks might try to compromise the account access or the email provider, which then allows them to trigger a password reset.

Email account compromises and email server compromises are still comparatively rare activities, though attempts to con folks into revealing their Apple ID passwords is common.