Whether a dependent or not, you still file stock sales the same way.
you need to file if you want to carryforward any losses.
If you had no other income you are below the threshold requiring you to file.
Yes, but you can't claim your own exemption. Somewhere early in the process you will be asked if someone else can claim you as a dependent, and you must answer that YES. This means you don't get the same standard deduction that a non-dependent would get.
Also, if your unearned income is higher than some threshold (I think $2200), you will be taxed at your father's rate. (It's called the "kiddie tax," and was designed to keep rich parents from avoiding taxes by putting investments in their children's names.) Presumably your tax software will catch this if it needs to, and guide you through it. With the low income you mentioned you don't have to worry about that.