Yes there are repair options but these are not run by default. There are REPAIR_REBUILD and REPAIR_ALLOW_DATA_LOSS options.
How about if the database has been mirrored?
Not sure what you mean? If you're asking whether you can run DBCC CHECKDB on a mirrored database, then yes, certainly you can (well I do!)
Measure twice; cut once (and have a good saw)
Hey, just a thought.....did you check Books Online yet?