Do arbitrary/Byzantine failures include omission failures and timing failures?
Arbitrary failure means exactly what it says. It means that the failing process should be treated as if an opponent is choosing the process's behavior to try to break your system.

Other types of failure, such as omission failures and timing failures, are special cases of this. They are relevant because certain algorithms only guarantee correct results in all cases if, for example, it is assumed that a process may fail to respond to a message (omission failure) but cannot fail in other ways, such as by responding with incorrect data.