Incorrect. "Where are you on Thursday? I'm at work" This doesn't necessarily mean the person is at work now
"В работе" can't be used for the 'place' meaning of 'work' - only for the 'process' meaning of 'work'.
E.g.: Я весь в работе - I wrapped up in work
Also "в работе" is used to describe the particular degree of readiness (not ready yet / on the anvil)
This dicussion is down to the fact that english has no verb endings for the future (such as -ed for regular past) so we use the present simple to talk about definite plans in the future. You're all kind of correct.