Year of Mourning for Parents

I am an avela, and in the first year of mourning for my father. Am I permitted to go to a meal out at a Kosher restaurant with my nephew? Also, for my birthday maybe with my sister? I want to honor my father and do always the right thing Also I don’t know if it is proper and permitted to buy new shoes for Tisha B’Av Thank you Rabbi for you kindness and help to me

You should not dine in a restaurant with your nephew nor with your sister until after the twelfth month. (Shulchan Aruch and the Rema Yoreh Deah 391, 2. and Shach 1. See also Penei Baruch reply letter of Rabbi Shlomo Zalman Auerbach Zt"l 3). It is best to buy shoes for Tisha B'Av before Rosh Chodesh Av. It is preferable if one would wear them on Yom Kippur for the first time. But if he does not have shoes which are permitted to wear on Tisha B'Av and he forgot to buy them before Rosh Chodesh, it is permitted to buy them after Rosh Chodesh and even in the week of Tisha B'Av, because it is difficult for him to walk barefoot only with socks. (Igrot Moshe Orach Chaim 3, 80. Kaf Hachaim 551, 96). May the Omnipresent One comfort you amongst the mourners of Zion and Jerusalem. (On a father or mother one can console all twelve months, Shulchan Aruch Yoreh Deah 385, 2).