MacBook won't update. It restarts, says it'll take several minutes to update, and then restarts normally. How can I fix this?

Are you using any anti-virus apps, cleaning apps, or third party security apps which may be interfering with the update process? You can try initiating the update from Safe Mode.

Did you try booting into Safe Mode before starting the update again?

If you did and the system still needs to restart after applying the update, then I suggest pressing the Caps Lock key before running the update in Safe Mode. Once the laptop reboots the Caps Lock key will go out indicating you need to press & hold the Shift key so that the laptop boots back into Safe Mode again (in case the installer still needs to update some system files).

If you still have problems, then run Disk Utility First Aid on the SSD (actually run it on the "Container" and not just the boot volume). Within Disk Utility you will need to click on "View" and select "Show All Devices" before the physical drive and Container appear on the left pane of Disk Utility. Even if First Aid shows everything as "Ok" make sure to click on the "Details" and review the details to see if there are any unfixed errors listed. If there are you will need to back up the laptop and erase the whole physical drive before restoring from the back up as this is the only way to have a clean file system.

Run EtreCheck and post the report here using the "Additional Text" icon which looks like a piece of paper.

If you still have problems, then exactly what update(s) are you trying to install?

Try manually updating Catalina using the Combo Updater:

https://support.apple.com/kb/DL2052?locale=en_US

Try installing the Safari update by itself. Maybe installing the two updates at the same time is causing problems.