Choices 2 and 3 are both partially correct. Migrated questions are copied over and do not synchronize between sites; the original is automatically closed on the original site. After a while, it is deleted from the original site.
Example: this question on Programmers was migrated to this question on Code Review. The original post was simultaneously locked by Community (a "moderator" that is actually a bunch of automatic clean-up processes built into the software). Eventually, the original was automatically deleted by Community.