Answers :
1.You might find a small notebook useful if you are forgetful.
  Correct.

2.A spoon is more useful than chopsticks when eating rice.
  Correct.

3.The Worst Case-Scenario Survival Book can be useful if you happen to be in such rare occasions as mentioned in the book.
  Correct

4.Hobbies make your time useful.
  Incorrect. This sentence is awkward; it should be ‘Hobbies make good use of your time’.

5.You should spend your time usefully. Do not be lazy.
  Incorrect. ‘Productively’ is a better choice of word.

6.I would like to buy something useful as your wedding present.
  Correct.

7.Having an Internet access is useful.
  Correct. You can also suggest ‘convenient’ or ‘handy’.

8.Your garden space is useful. Children can play there, or we can have parties there.
  Incorrect. ‘Functional’ is a better word.