If you add dry base rock to a tank with livestock, it will be fine. Rinse it really well in RO
water and maybe give it a quick scrub to get some of the dust/loose stuff off. It will become live in time.
Moving live rock from tank to tank can be a little more tricky. A lot of times LR
has dead matter on it, stuck in crevices/holes/etc. When you go in and take it out and dunk it in another tank, you can release a lot of that stuff and cause an ammonia spike. LR
from one tank can also have algae spores, hydroids, flatworms and all sorts of other things you may not want to spread around. You should always rinse and scrub when moving rock and still pay very close attention to your levels. Scary stuff aside, if you take proper precautions, LR
is fine to move from tank to tank.