Your father did his duty by paying khums on what was liable for him. Once he transferred that amount to you, it now becomes your responsibility. In regards to gifts and khums, this depends on taqleed, so you will need to refer to your Marja' taqleed to see if khums is liable on gifts.
Every one is allowed to give charity from his own earned income with out permission from his father or mother etc as far as his father and Munther are not in need for that charity money for their own livelihood expenses.
If your father gives you the pocket money as a gift for you with out any condition, you can then spend it as you wish in lawful expenditure or save it or invest it. No one will have then right on that money or ask you to return it. If your father gives you pocket money for spending and not for saving or investing, then he has right to ask you to use it for your expenses only and return the amounts which were not used in your expenses.
Most of parents give their children pocket money with out condition.
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