1. When to use be going to + infinitive?
Use it for future plans and intentions.
Use it for predictions.
We use going to (NOT will / won't) when we have already decided to do something. Wrong: My sister· will adopt a child.
We also use going to to make a prediction about the future, especially when you can see or have some evidence (e.g. black clouds).
2. When to use present continuous: be+ verb + -ing?
Use it for future arrangements.
We often use the present continuous for future a rrangements.
There is very little difference between the present continuous and going to for future plans/ arrangements, and often you can use either.
Going to shows that you have made a decision.
The present continuous emphasizes that you have made the arrangements.
We often use the present continuous with verbs relating to travel arrangements, e.g. go, come, arrive, leave, etc.
3. When to use will/shall+ infinitive
Use it when you make instant decisions, promises, offers, predictions, future facts, suggestions
We use will/won't (NOT the present simple) for instant decisions, promises, offers, and suggestions.
Wrong: I carry that bag for you.
We can also use will / won't for predictions,
... and to talk about future facts.
We use shall (NO will) wih I and we for offers and suggestions when they are questions.
Source: English File, Intermediate
by Chritina Latham-Koenig and Clive Oxenden