Let's analyze each sentence step by step. For sentences marked in bold, we will determine if they are correct. If a sentence is incorrect, I will rewrite it correctly.
The universe is going to continue to expand for billions of years.
Correct: +Look out! You will hit the car in front!
Correct: +I’m going to do the washing-up tonight, if you like.
Correct: +Do you think that, in the future, people will live to be hundreds of years old?
Correct: +Will I carry some of those bags for you, or can you manage?
Correct: +I know! I'm going to have a barbecue on my birthday.
Correct: +Are you going to just hold this door open for me for a minute? Thanks a lot!
Correct: +We've decided we will try that new restaurant after the play tomorrow night.
Correct: +We're going to fly to Jamaica in the summer.
Correct: +Shall we invite Tony and Tim round tonight?
Correct: +Are we going to invite Tony and Tim round tonight?
Correct: +Will you go to Jason’s party next Saturday?
Correct: +
All sentences are correct as they stand. If you have any questions or need further clarification on any specific sentence, feel free to ask!