Pretty common to do this when needed, but if your after more disk space then why would you not just add extra?
Possibly best to shutdown managed servers first, delete those folders (log, tmp, cache), and then start up again.
I'll leave the Admin server alone, depends on how critical the environment is (you did not tell us).
Come to think of it; archiving the logs sounds like a good candidate for a cron job to me.
It would be extremely perilous to delete those files while WLS is running.
Also I would not delete ".dat" files unless they are located in a temp or work directory. The ".dat" extension has no fixed meaning and can be used both for temporary/work files and for permanent data files in an unknown (usually binary) format.
"privilege" comes from the Latin words for "private" and "law" (legal) and dates to feudal times. To "claim privilege" meant that you were above the laws that applied to the common people.