The 'normal' setup for an AIX system is to divide the system software and the appliaction data into two different volume groups. The system software will be in rootvg, the aplication data will be in, for example, datavg. There are differing reasons as to where to put the application software, personally I plump for datavg.
Having said that the mksysb backs up rootvg only. Under normal circumstances changes in rootvg will be limited to user details, passwords etc and, as such how often you should back up depends on how much you want to say to your user base "all changes in users, passwords etc. have been reverted to the last backup." Our main systems have mksysb's taken using NIM on a nightly basis, one of our little used dev systems only has a mksysb when there's a change applied.
Having said that you should always do a mksysb before applying patches, etc. Patches are, by their very nature, applied to system software in rootvg and, if you have to revert, restoring a mksysb may be faster and easier than rolling back numerous patches.
Can you do a mksysb with the system up - yes, as long as the application is in a different volume group.
A mksysb is not the be all and end all of system backups - it only does the system software. It is the norm to use some other product to backup the datavg depending on the size and complexity of the job. It is common to have to stop applications before doing this type of backup but that is application dependant.
I hope this helps
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