Here are the corrected sentences with the mistakes fixed:

1. It will be very cold this evening, so you should wear a coat. (removed "is")
2. Do you think we will be living on another planet in the 22nd century? (added "be")
3. He will save money to buy a new bicycle. (changed "saves" to "save")
4. I think that newspapers will not disappear because of the Internet. (rearranged "not" and "will")
5. Will they open a new supermarket in our neighborhood? (removed "to")