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Some very long answers...let's be brief.

 

1. If your child can be claimed as a dependent, he must answer "I can be claimed as a dependent" on his tax return if he can be claimed, even if he doesn't want to be claimed. (See the rules below.  You are not required to actually claim your child, but even if you don't for some reason, they must answer they can be claimed if that is the case.) 

2. You can file as HOH if you 

a. actually claim your child as a dependent

b. your child lives in your home more than half the year

c. you pay more than half the cost of maintaining the household.

3. You can't claim your child as a dependent if your child answers "No, I can't be claimed as a dependent by someone else."  That will raise a red flag and be blocked and investigated by the IRS.