Hello,
1) If I attach my old Witty Pi 3 to a RPi will I be able to access the DS3231 without any interference? Witty Pi 3 application software not loaded to the RPi.
2) Would Power be applied to the RPi, or the Witty Pi 3. Would it matter?
The DS3231 on Witty Pi 3 is directly connected to Raspberry Pi's I2C bus, at address 0x68. You can access it without Witty Pi 3 software, provided the RTC is properly powered and I2C is enabled.
Please note that daemon.sh runs automatically in the background after the Witty Pi software is installed. Simply not running wittyPi.sh does not prevent the daemon from accessing the RTC. If you no longer intend to use the Witty Pi software, I recommend uninstalling it completely.
Normally, power should be supplied to Witty Pi 3, which then powers the Raspberry Pi.
If you power the Raspberry Pi directly instead, there may be a reverse current path through the power-switching MOSFET that allows the Witty Pi 3's onboard 3.3V regulator to power the RTC. However, this is not an intended or tested operating mode, so I cannot guarantee that it will work.
Since your Witty Pi 3 may already have a hardware fault, you would need to verify its actual behavior yourself.