Is the beta program safe to install as in good security and won't damage my phone or my other apple products I have?

First, do not install a beta version on your primary phone. Use a secondary phone so that if you find a bug, it won’t affect your ability to use your main phone. The beta test program is meant to find bugs and other issues before the final version is released. It is as safe as it can be. It will not affect any other devices that you may have.

Safest to use only on a secondary device and not your daily driver.