Living at college is considered a temporary absence so you are still counted as living at home. If you are under 24 years old, a Full-Time college student, do not provide more than half of your own support and no one else is claiming you on their return, then your mother can still claim you.
If you have no income, you will not file a tax return. A stock purchase is not reportable. When you sell your stock, you will report it then.
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