nope, mice can actually find their way back to your place, and if you let them at other place, u will cause trouble to people living there.
The best way to kill them is to hammer the head so they die instantly, though I have seen effective way of drowning them in the drain, that my friend sounds evil, but wait till u see people incinerate them,
it is not cruel to do that since they are pest, if you can feed it to the phyton that will be better.
one thing about pest is they have no natural predator/disease that is really into them, try introducing an owl or raven to ur house to see a decline in the population

btw the big house rat is not actually local in malaysia, they are introduced animals, accidentally brought in by traders via their ship. ( i do not have source for this, but I believed I have read it somewhere)