Insalled Catalina and get very many beach balls

Your computer is starved for RAM. Please upgrade to 16GB or more. If you do, please only get crucial.com or macsales.com RAM . Both vendors supply high quality products, very fair prices and have excellent service. In short there is no reason to not use them.

The new macOS has several back ground tasks to carry out. Be patient, because depending on your data and Mac spec's, it can take anywhere from an hours to a full day to complete those tasks and settle down.

If you're curious, you can use the CPU section of Activity Monitor to monitor those back ground tasks.

How to use Activity Monitor on your Mac - Apple Support

You have it backwards, many programs are not compatible with Catalina, at least their 32 bit versions. iDVD was discontinued close to 10 years ago, really you are blaming Catalina for that. And I'm willing to wager that TT, TW and even SuperDuper all have 64bit versions. Apple has advised you for over a year that 32 bit apps won't run on future (Catalina and beyond) versions of Mac OS. Sounds to me like you just ignored the messages!

Unfortunately that is a short sighted approach as eventually you will need to upgrade to another Mac and there is no way a new machine will run an older OS. Why not move forward and just find a replacement for iDVD, there are many many out there.

Did you empty the Trash???

Did installing more ram solve your beach ball problem ?