I had a chat with an Apple Support specialist early this week. He was very helpful, courteous, a professional in his field; as always, including the Genius personnel at the Apple Store when I had questions regarding several issue(s) with my Macs.
Long story short: the Apple specialist covered all the basic pre-macOS Catalina install procedures, including post Catalina troubleshooting basic procedures. Such as:
Pre-macOS Catalina install (upgrade) procedure:
1. Making sure the boot HDD or SSD is free of errors; boot procedure regarding using Disk Utility, Check / Repair ==> About macOS Recovery https://support.apple.com/en-us/HT201314; if ok, next procedure
2. Uninstall all third party apps that didn’t have an option to update / upgrade in order to be operational on macOS Catalina. Note, these are actually 64 bit applications that eventually do not have the latest (necessary) updates to run trouble free in macOS Catalina.
After Catalina Install - basic troubleshooting procedures:
1. How to reset the System Management Controller (SMC) on your Mac: https://support.apple.com/en-us/HT201295; if not ok, next procedure
2. Follow instructions on how to Reset NVRAM or PRAM on your Mac: https://support.apple.com/en-us/HT204063; if still not ok, next procedure
3. Repeat Disk Utility, Check / Repair procedure (link above) to make sure the HDD or SSD data is still pristine.
4. If all of the above don’t clear the issue(s) ==> Create a New Administrator account to check if the issue is encountered in that new account. How to test an issue in another user account on your Mac: https://support.apple.com/en-us/HT204443
Note, I have created a new admin account and the Kernel panic and crashes went away. Also, you may want to use an application that points out the issues, like EtreCheck for example, and get to know what causing Kernel panics and crashes, including beachball spin errors and crashes. Work from that app generated report to get information on available updates or upgrades on the apps in question. If no further updates or upgrades are available, see if the app can be removed by means of conventional uninstall option. If that is not available, search for manual alternatives to remove the app and any orphan files left behind from an incomplete, (rather partial) uninstallation(s); (Note, "Cleaner" like apps might not work 100% in new macOS Catalina; most importantly, not recommended).
In My case, I found some some launch agents like I.e. “com.paragon-software.ntfs.notification-agent” by Paragon Software GmbH, and “org.macosforge.xquartz.startx” ==> Install date Xquartz is 2016-10-26 02:57:09. So, Xquartz has to go since is outdated - I week before I thought it was removed, but… I have no explanation on how it got back.
Hope this helped. Regards.