Hi Lahm08
welcome to the Apple (user-to-user) Community.
Re: "Imessage issue: All of a sudden, I'm unable to use imessage on my mac, same as my phone".
Check you are signed in (to your iPhone) and (to your Mac) with your correct Apple ID:
How to: Sign in with your Apple ID - Apple Support
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Wondering which iOS version is installed on your iPhone 14 Pro:
Eg: Apple support's article About iOS 17 Updates - Apple Support says iOS 17.3 is the latest update.
"This update introduces additional security measures..." :
To check if the update is waiting to be installed, try: Settings > General> Software update
Else if you are already using iOS 17.3 on your iPhone:
Try restarting your iPhone: Restart your iPhone - Apple Support (re-establishes connections, deletes temporary files, often restores order.)
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Re: "On mac, I can't set it up at all. I need help please and who knows what might be the issues".
On Mac: Check whether an update is waiting to be installed:
Eg: Apple menu > System Preferences or System Settings > General > Software update.
If your Mac has the newest compatible update already: try Apple menu > Restart
After waiting for Mac to restart: Log back in to your Mac and check if Messages works ok.
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Re: "Although once a while the messages get delivered as Blue, but most times its green".
Green bubbles are text messages using cellular data. (Eg: Android phones)
Blue messages are iMessages from Apple to Apple devices using wi-fi.
See: What to do: If your iPhone or iPad won't connect to a Wi-Fi network - Apple Support
and
Connect iPhone to the internet - Apple Support
You may need to restart your modem / or check with your internet provider
If you can’t connect to a Wi-Fi network on Mac - Apple Support
or
If your Mac isn't connecting to the internet over Wi-Fi - Apple Support
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Re: "I can't log in or connect icloud to the "messages' in settings".
You may need to check if you are connected to wi-fi
Else, if connected ok:
See: What to do: If you can’t turn on or sign in to iMessage or FaceTime on your iPhone - Apple Support
and
If you can't sign in to your iMessage account or FaceTime on your Mac - Apple Support
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If needed:
How to: Set up iCloud for Messages on all your devices - Apple Support
Apple Messages Support Webpage: (info / support / contact options etc.)
Messages for iPhone, iPad, Apple Watch, and Mac - Official Apple Support
All the best :-)