I have read discussions on NOT to use external power, say an ac adapter, instead of the 9V battery. But what if I mostly do is to test for continuity, would it be acceptable in such case? What other alteratives are possible, such as the 6 x1.5V cells battery case or most recently, use Li rechargeable battery (for phone use) (2 x5V or what? ) for this purpose?
I have read discussions on NOT to use external power, say an ac adapter, instead of the 9V battery. But what if I mostly do is to test for continuity, would it be acceptable in such case?
If you are only using the multimeter on circuits that are safe to touch it should be no problem to run it off a power brick (assuming the power brick meets normal safety standards) or a 6xAA battery box.
The problem comes if you are using the meter on circuits that are not safe to touch. The electronics of the multimeter are connected to the input terminals and therefore during work on circuits containing dangerous voltages the internals of the multimeter including the battery will become dangerous to touch.
That is ok if you are using the multimeter as intended, the enclosure of the multimeter protects against contact with live parts* but if you compromise the electrical isolation of that enclosure (for example by running a cable through it to a power brick or an external battery holder) then the meter will no longer meet it's safety standards.
* This BTW is why modern multimeters always require a tool to change the battery.