How can I delete all case comments that are in application in a quick way? Is there even a quick way?
If there are a lot of records (>10.000) it's best to use DataLoader to first retrieve all CaseComment record Id's, then delete based on that output file.
If the amount is under 10.000, you can do the following from the 'Execute Anonymous' window in the Developer Console:
delete [Select Id From CaseComment];
Optionally you could split that up into chunks of 10.000. You'd have to run it a couple of times then:
delete [Select Id From CaseComment LIMIT 10000];