Recently, certain functions on my iMac 18.3 have changed in a strange way.

1).
The iMac can no longer be turned off going through the Apple icon at the top left -> Turn off, but restarts instead.
The only thing that helps is a hard shutdown using the PWR button.

Turning off by using the selection menue on the logon-desktop (Turn off - Restart - Hibernate) only leads to a restart too.
Restarting via the menues - either Apple-icon or logon-desktop - works normally.

All attempts using NVRAM reset, SMC reset did not improve the situation.

2).
Installing macOS Ventura, Monterey etc. only goes up to the 2nd phase of the installation - after rebooting again, the macOS installer suddenly disappeared and is no longer displayed in the Apple picker via ALT. Only already installed/existing macOS were displayed.

Installing a new macOS on the iMac data storage device is only possible by using an external case and then connecting it to the iMac (USB-C).

Once installed the data storage back into the iMac, booting is possible without any problems.
But adding another macOS while the disk is installed again is still not possible.

Everything else works as usual.

Any advices, tips on how to solve the problems would be appreciated. Thanks.