It’s one of the ways of talking about the future, but there are a few others. Let’s look at will to start with. We use will / won’t (= will not) + the infinitive for predictions about the future.

Oliver’ll be back soon.
We won’t be ready.
Do you think it’ll rain this afternoon?

We also use will when we decide something at the moment of speaking.

(The doorbell rings) I’ll get it.

Yes, that’s very common. We also use: don’t think, expect, be + sure.

I’m sure you’ll have a good time.

Then we can use either the present continuous or going to (+ infinitive).

Amy’s coming round.
We’re going to watch a film – want to join us?
What are you doing this evening?    

We use the present continuous more for arrangements with other people and be + going to + infinitive for intentions. Sometimes it’s important to choose the right structure, but often we could use either because many events are both arrangements and intentions.

Amy’s coming round. (= arrangement between Amy and Daisy)
Amy’s going to come round. (= Amy’s intention)
I’m going to clean my room tonight. (= intention)
I’m cleaning my room tonight. (not an arrangement)

Yes, that’s correct. But we usually avoid saying going to go, just because it doesn’t sound very elegant. We normally use the present continuous with go.

I’m going to the cinema with Alex.

No. We don’t use will for arrangements or intentions if the decision was made before the moment of speaking.

Yes, there’s another use of going to. We use it for predictions too, especially when you can see something happening or about to happen.

Look out! You’re going to spill that coffee.

Yes, sometimes both will and going to can be used.

I think the Green Party will win the election.
I think the Green Party are going to win the election.

Yes. You can use present simple for timetabled events.

My plane leaves at 4pm tomorrow.
The match starts at 8pm.

I’m sure you will! You’re using it correctly already.