I just flashed LOS 20 on my 7 pro the other day. I already had experience with flashing LOS before. But their guides make it pretty easy and straight forward though. You can read it here: https://wiki.lineageos.org/devices/guacamole/install

to 2) if you want google apps, such as playstore, you actually have to flash gapps additionally to LOS. But that's all mentioned in the guide.

to 3) I only have experience with LOS, but from my limited use the last few days I have to say that it feels very smooth and stable. It is night and day to the bugy mess that was Android 12 on the 7 pro. Also I really like the design and the new animations of Android 13. But I miss a few oneplus specific features, e.g. Ambient Display. I also feel like my battery drains a little bit faster, but I'm not 100% sure about this yet.

to 4) LOS offers OTA updates. From my past experience with LOS I can say that there probably will be updates for a long time, especially for popular devices. If you look on their webpage you can see they still support pretty old devices too.

I also have to mention that there seems to be a bug when trying to unlock the bootloader with the current oneplus Android 12 version. I actually had to downgrade to Android 11 then unlock bootloader and then update to Android 12 again before flashing the custom rom.