It is highly recommended to mourn for Imam Hussein and his near and dear ones on the months of Muharram and Safar and infact all through the year. There is no grief comprehendible like grieving for the Prophet and his.pure progeny. It is also recommended that if one were to cry for their lost ones, they should remember the Ahlbayt a.s and also cry for them. This makes the bereavement reach higher reward and acceptance.
It is completely alright to remember your near and dear ones by praying and reciting Fateha for them and the best way is to first grant your prayers as a gift to the Ahlbayt a.s who will then in turn give the reward to the deceased in a complete and perfect way as suggested by great scholars.
In any case, reciting fateha for your father is still a great reward because the words and prayers are from no other source but the Almighty Allah whom the Ahlbayt were united with so it is also a way to earn their pleasure.