I'm in the school.
Means I am in the building (but I may not be a student).
I'm in school.
Means I am attending school (I'm a student).
- I'm working
- I am at work
3 and 4 can be equivalent in meaning, just as the first dictionary entry suggests, and neither would be "more" correct. In other words, they can both mean "be busy doing their job right now". The problem is that 4 can easily be understood as 2 in the entries given. So I believe it would come down to context.
If your friend comes into your office, or place of work, and says "Let's play basketball" and you respond, "Not now, I'm at work", then he can see that you are working and deduce from context that you mean "I'm working".
If your friend calls you, or otherwise can't see you, and asks to play basketball, and you respond "Not now, I am at work", then it sounds like you are saying that you are at your office, or place of work. This strongly suggests that you are working, but it's not necessarily true.
In any case, if you want to be clear, I would recommend "Not now, I'm working."
Best Answer
When you are new to something, you are a beginner at it. So to say that you are new to this town means that the town is something to be learned. You are just learning about the town and its ways, only beginning to acquire the knowledge and skills required to make your way in the town, to be a success there.
A singer might say of Nashville:
and thereby mean that there are things a singer must learn in order to succeed in Nashville.
A newly elected member of the House of Representatives might say of Washington DC:
and mean much the same thing.
When we are new in a place, we are newly arrived there.
P.S. to can impart to "new" the connotations of "inexperience" by virtue of the fact that the collocation new to is very frequently used in contexts where the speaker wants to express not merely the idea of novelty but the idea of novice or neophyte.
Those endeavors are not merely novelties for her; she is a beginner at them.
The pattern puts "the big city" in the semantic role of "thing-to-be-learned".
P.P.S. Consider that we would not say:
but
P.P.P.S. But that is not to say that new to the taste is impossible. Consider a discussion of so-called "acquired tastes", tastes that most people don't like but some come to enjoy.