A:
It depends on what was pending at the time the motion to Adjourn was defeated.
For example, if a main motion was being debated at the time, then almost any motion would be in order except another main motion and the motion to Adjourn.
If Adjourn fails, the situation is almost as if the motion had never been made.
The assumption is that the assembly is not ready to conclude, that it wishes to continue.
Adjourn is not immediately in order because the assembly just decided not to adjourn; however, it will be in order after the parliamentary situation has changed (such as after more debate is heard).