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Please read 2 examples and my description of meaning. Am I right? If you could add something, please do it.
Next week she will be in London.
At now she decides that she will be in London next week, she must be there next week.
Next week she is going to be in London.
She has an idea to be in London next week and she will try to do it but not obligatory if plans are changed.
The truth is that there really is not much difference between "will" and "is going to" in modern English. They basically mean the same thing to most people.
Various grammarians like to talk about subtle differences in meaning or intent between the two, but those are usually lost on anyone who hasn't spent a lot of time studying language, etc, so it's not a good idea to try to read too much meaning into the choice between using these two verb forms.
So, your two sentences really mean the same thing. Neither one says anything really specific about intention vs. reality. They both just say that (it is expected that) she will be in London next week.
For most people, "is going to" is just a more casual way to say "will". Since it is more casual, it's not used as much in formal writing, etc. Conversely, "will" often has a more formal sound, and people often prefer "is going to" in casual conversation.
Technically, "is going to" says that somebody intends to do something, while "will" says that it will actually happen, but in practice that distinction (if it exists at all) is very subtle and usually not that important.
“She is planning on being in London next week, but her plans may change.”
Or
“She will be in London next week.”
“Next week she is going to be in London”
also works, you got that one right.
The others are incorrect; instead of “she has an idea to be in London” you might say instead;
“she is thinking of going to London”.
