The Champions League has been eliminated to the previous 16. After the last 1/8, there will be another draw. After that, the schedule will be played in the order of signing. If both games are 0-0, as you said, there will be an overtime first, and then a penalty will be taken after the overtime.
The Italian Cup was played directly according to the schedule, and all of them were eliminated. If both games are 0-0, play an extra time first, if the extra time is 0-0, then play a penalty shoot-out.