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Here are the corrected sentences with the appropriate use of future forms:

1) The sun's shining brightly. So, if it stays a beautiful day, I'll ask her out for a date. I'm playing football this afternoon. Do you feel bad? (Are) you going to come?
2) Their trip got cancelled, so they're not going to take them to the station.
3) We've run out of sugar. No problem, I'll go and buy some more from the store.
4) The author will explain this mode next week.
5) Hal is studying medicine. He is going to become a doctor. Wow! Look at the flowers! They are going to blossom.
6) Tom is making a pond. He is going to dig a hole in the ground and fill it with water.
7) They are celebrating their anniversary this week, and I need to book a restaurant for them.
8) It's too cold. I am going to close the window.
9) Jennifer is flying to Egypt on Saturday.
10) Ben is at the post office. He is going to post a letter.
11) Tonight we are having dinner with the Smiths.
12) Ann is visiting Paris. She is going to see the Eiffel Tower.
13) It's sunny outside. I am going to wear my sunglasses.
14) This suitcase is too heavy! I am going to help you carry it.
15) We haven't got any oranges. Are you going to buy some?