>• If we let the cells repair it by themselves, will they not just remake the segment we just cut off?

Depending on the strategy used, they often do just that. Afterwards, you can just select the cells that used the repair template with your insert.

>• If we insert a new gene, how exactly do we deliver it? Does it come with the CAS9 and guide RNA complex? Or do we use another enzyme to deliver it separately?

Traditionally it's a separate piece of DNA we deliver. But prime editing actually delivers the template as part of the guide RNA. That only allows fairly small edits though.