Incorrect. "Where are you on Thursday? I'm at work" This doesn't necessarily mean the person is at work now
"Where WERE you on Thursday? I WAS at work". "I'm at work" absolutely implies you are there now.
There would often be an added implication in the English usage of "I am at work now" which is expressed by the now. Maybe you have just arrived at work, or might not be there in a few minutes, or perhaps that because you are at work, this is not a suitable time to be discussing personal activities, so come back later. The now emphasizes the transitory nature of this status. I don't know if the same thing is true with сейчас in Russian, but it wouldn't surprise me.
I'm pretty sure «в работе» literally means "inside of work" instead of "at work"
"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.