Since this is a tax forum, we may not be much help with financial aid forms, there are likely counselors at school for that.
Regarding taxes:
Your grandson is your tax dependent on your tax return if he meets the following tests. It is not necessary that you have any kind of court order or adoption placement.
Your grandson will file his own tax return for income in his name, including wages and investments. The fact that he files his own tax return does not interfere with your ability to claim him as a dependent as long as he provides less than half his total financial support. If he is your tax dependent, he must answer "yes, I can be claimed as a dependent by someone else". If he has investment income, or is trying to qualify for certain education credits, he may be asked for information about his parent's income--those questions do refer to his parents and not to you.
When filing financial aid forms, I suggest he read the instructions or ask a financial aid counselor. Or maybe someone else here will know, I do not.