1- Prophets inherit just like other people. There is no verse or hadith that states they don’t leave any inheritance. Yes there is a hadith that states their inheritance is knowledge (it’s a symbolic way to say that their goal wasn’t to gather money and leave it behind like kings do). Also Naml 16 states that Sulayman inherited Dawud
2- The Prophet gave Fadak to Fatima in her lifetime. She owned it. Assuming they reject that, then she is the sole inheritor. So no matter how you look at it then she owned it
3- Why did Aisha use the Prophet’s room and have her father and Omar buried there (as Sunnis claim he died in her house)? How did it become her personal room? If they claim he gifted it to her let them show evidence. If they say it’s inheritance then I thought he doesn’t leave any inheritance!