If your child starts working at 16 can you still claim them as a dependent?

Yes and you can even claim their income if no federal taxes have been taken out. He can be claimed up to age 19 if he is a full time student.

Yes you can, but you have to pay for at least 51% of their living costs. The dependent must be under 19 (or under 24 if they are student), or any age if they are disabled. This is how people are able to claim their aging relatives as a dependent. A social security number will always be required for each dependent.

The social security requirement started when people started claiming pets as dependents.

As long as they live with you for more than half of the year and you provide more than half of their support you can still claim them as a dependent.

Yes, if they live with you for over half the year, and don't provide over half of their own support for the year.

If the child files their own return, they note on it that they can be claimed as a dependent, and they don't get an exemption for themselves since the parent gets it.

Yes. You can legally still claim them as dependents as long as they are in school and not married up until 23 (It may be 25, but I'm pretty sure it's 23.)

You can legally claim them until 18, working or not, or 23 if he/she is a full time student. However, if they are having withholding tax taken out of their check, you need to figure out at tax time if it is more beneficial to you to claim them, or let them claim themself on their own tax return.