Hi angelaxz
welcome to the Apple (user-to-user) Community!
Re: " ... about two months ago FaceTime just stopped working.
There are many possible causes; finding the cause may solve the issue:
See if Apple Support's online articles (links below) may help trouble-shoot
Wondering which MacOS version is installed on your Mac:.
You can check for updates in System Settings > General > Software Updates.
If an update is waiting to be installed, it is wise to back-up your data first, if you choose to update / upgrade.
If you are using the most up-to-date MacOS already, you could try restarting your Mac: (deletes tempoorary files, re-establishes connections, may update recent setting changes, often restores order if someting is not working as expected.) Choose Apple Menu > Restart ... wait for Mac to restart and log back-in. Test if FaceTime.is working.
Still need help?
You may want to check to make sure everything is still as required :
See: FaceTime requirements on Mac - Apple Support
To check that you are signed in to your Mac with your correct Apple ID:
See: Sign in to your Apple Account - Apple Support
Make sure your wi-fi is working ok on your Mac, you may need a strong signal for FaceTime.
If you use VPN, try turning it off, while you check if FaceTime is working when it is off.
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To look up anything about FaceTime as needed: See the "Table of Contents" in the linked User Guide below.
Resource: FaceTime User Guide for Mac - Apple Support
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Re: "At best I can open it but I can’t pick up any calls let alone make them on the device.
I always have to force quit the application or it force quits on its own."
See what to do: If you can't make or receive a FaceTime call on your iPhone or iPad - Apple Support
and
If needed: Set up your iPhone and FaceTime on Mac for phone calls - Apple Support
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Re: "I’ve repeatedly reported the issue to Apple (not sure if that actually does anything, first time using a Mac)
and nothing has really changed. "
There are many possible causes of your issue ...
If you contacted Apple Support and were given a case number:
You can sign in to view up-to-date information on a tech support case.
My Support - Official Apple Support
If you sent feedback to Apple, it reaches those who can make software changes.
If others also have similar issues. they may be addressed in a future update.
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Re: "I’ve held off on trying to seriously get it fixed just because I can still make the calls from my phone".
"I really don’t think a brand new laptop should have so many software issues…"
During the first 3 months with a new Mac complimentary hardware and software support is available.
Learn more about complimentary technical support (select your country or region for support)
Apple One-Year Limited Warranty and AppleCare Plan benefits are in addition to rights provided under consumer law. For details, click here
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Re: :Does anyone else have this problem?
As Apple users, like yourself, we do not get to see feedback sent to Apple. Unless someone with a similar experience replies to you here, we have no way of checking this out for you.
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Re: "Do you know if I’ll run into any more? "
No. Everyone's experience with a new Mac is unique.
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More info./ support / contact options if needed:
The FaceTime Support Team's Website: :FaceTime - Official Apple Support
All the best :-)