ESL, that is an amazing quote, which I’ll use to defend my preference for not discarding “whom” altogether.
I will no longer state to any students that “that” is incorrect for people. I agree that it is confusing to teach style as grammar, which occurs far too often, and this is an obvious example.
Ahmed, all the “work” sentences would be correct. The difference is the degree of certainty you want to express. If you want to state that you are absolutely going to work tomorrow, use the other examples. If you want to indicate that is merely what you expect to do, use “plan.”
I am not sure what you mean by “may be.”
“I may be going to work tomorrow” is not the same as “I plan to work tomorrow.” The latter indicates that it is likelier that you will. With “may,” it may even be likelier that you won’t go.
“I intend to work tomorrow” is close to “I plan to work tomorrow.”
If “may be” means “maybe” or “perhaps,” then I think you are suggesting “I am planning” as a substitute. In that case, the meaning will be preserved.