Hello!
1. Look at those clouds! It's going to rain. √ (use 'going to' for predictions!)
2. Will you read the text aloud, please? √ (volition will - you kindly ask the subject if they want to read the text aloud.)
3. Why did you buy those eggs? √ (this sentence is a little ambiguous, I would suggest the use of the present perfect, supposing the eggs are still in the frame at the moment of speaking - Why have you bought these eggs?) I'll make a cake tomorrow. × (use the present continuous, as the sentence refers to a personal plan - I'm making a cake tomorrow.)
4. This bag's very heavy! √ I'm going to help you. √ (premeditated intention)
5. Will you drive, please? I feel very tired. √ (volition will - Do you want to drive, please?)
6. Are you going to sign here, please? × (use volition will/would, preferably 'would', as it is more polite - Will/Would you sign here, please?)
7. Why do you want a torch? Will you explore caves? × (use 'be going to', as it is a premeditated intention - Are you going to explore caves?)
Good luck!
