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.
The property where you reside at as your home is exempted from Khums as far as you reside at it. The property which became a rental property must be calculated in your Khums.
Your near family members e.g. your parents, your wife and your children must be supported financially by you from your own money and it is not allowed to give them from Khums.
Other poor relatives can be helped from your own money and it will from the best charity. If you can not help them from your own money, you can give them from Sadat share if they are deserving pious needy Sadat. If they are not Sadat and need help and no one is ready to help them, then you can seek permission from Marje' of Taqleed to help them from Sahm e Imam (AS).
If you need to buy a house for livening in it and not for investment, and you have legally and islamically entered in the purchase agreement but the completion (full payment) was after your date of Khums, then the amount of the completion of the purchase is not under your free ownership because you have a binging agreement to pay. This makes that amount out of Khums calculations of that year because it was already committed for buying a house to live in.
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