Upgrade MacOs on older Macbook Pro

Have you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

1. No.

2. For updates, generally not; it can still access many of Apple's online services.

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Do you have newer versions of macOS and/or iOS and have contact key verification turned on? that might explain your issue logging into Messages.