No
If the student is over 18, they are an adult; therefore, if they received medical treatment, they are legally responsible for the bill. The fact that they are a dependant doesn't matter.
yes student responsible
Yes, parents are only legally responsible for minors.
because the teacher as a second parent of the student is also responsible to provide parental care.
Yes, they can tell them to leave. Once the child is an adult, age 18, the parents are no longer legally responsible for them. They can even charge them with trespassing if they don't leave.
I believe the answer is no. Any contract with a minor, whether written or verbal, is unenforceable.
No, not legally.
The student
One can apply for a student credit card when one is legally considered an adult. In the United States, that is eighteen years old. Prior to that, teenagers may use credit cards if their parents are responsible for the purchases and payments on the card.
A teacher is not allowed to get involved with a student legally and especially not a student who still is a minor.
Your student was not actually responsible for composing this sentence.
18