[SalesForce] Prevent Process Builder action from firing when lookup field is blank

A quick change would be to add a Checkbox field on Opportunity. When you send out emails, you mark that new field. When specified changes have been made to the record AND the checkbox is unchecked then send out emails.

If there is more nuance than that like needing to send these emails out more than once if a record is updated later then I would suggest utilizing a flow to handle more complex conditions.

Process builders, Workflows and Triggers are fired only when there is a change made to the record i.e. only when a DML operation is performed on the record.

Your checkbox formula does not have any issues and it correctly checks the checkbox after 3 minutes (when you refresh the page), in the same way your criteria node formula also doesn't have any logical issues, only problem is that your criteria will never meet when process builder is invoked. And that is because, as mentioned, process builder is invoked when record is created/edited, and when it is created/edited, ((NOW() - [Case].LastModifiedDate )*24 ) > 0.05 will never be evaluated to true as the difference would be in milliseconds. And it wouldn't be called again unless an edit is made to the record. So, whenever an edit is made, it will check the criteria which will always return false.

For your requirement, you will have to go with Scheduled Actions in process builder, wherein you can specify the criteria as [Case].LastModifiedById = [Case].OwnerId and then run your action after X hours/days from Now.

You can get more information on how to set the scheduled actions in process builder at this trailhead link.

Note that currently process builder only allows to set scheduled actions in Hours and Days.