A woman's boss invited her to attend some business dinner and she asked
and I fit into this how?
Is it same with
How do I fit into this?
Expressing a question by using the normal word order for a statement but adding the appropriate question word at the end is a common, but not usual way of doing things. It is more common in some dialects, including some ethnic communities in English-speaking countries, and more uncommon in some other dialects.
In the increasingly popular "average English" that seems to be becoming more common in culturally European English-speaking countries, it is mostly used to express to express scepticism that the question will have an acceptable answer. This usage usually involves the question starting with and. For example:
And people get into the building where?
This might be asked by someone who's been shown a mock-up of a new building, or floor plans, and there is no obvious entrance.
And you are telling me this why?
This might be asked by someone who's just received information from someone, and they can see no reason that the person thought they should be given the information.
And I will buy this food with what?
This might be asked by someone who's been instructed to buy food, but not given the money to buy it. If it would be reasonable for them to be expected to pay for it themselves, it might be a pointed reminder that they could pay for it themselves if they weren't broke.
And I will be able to understand him how?
This might be asked by someone who has been told to go speak to someone who doesn't speak the same language as them.
There may be a pause immediately before the question word, but this is not essential.
Hopefully, those examples and explanations will help make things clearer.
You are correct. It is idiomatic (a "way we say things") to use question words (how, where, when, why, what, etc.) at the end of a sentence. The sentence is always reversible.
And I fit into this how? = How do I fit into this?
And you want me to be where? = Where do you want me to be?
You want to do what? = What do you want to do?