The various tribes in Afghanistan and Western Pakistan, mostly Pashtun, are always fighting with each other, even if many of them are "Taliban." One of the problems with the NATO occupation of Afghanistan was that it prevented the rival Pashtun tribes from establishing a competitive equilibrium with each other through various levels of conflict. Some of the tribes are allies of the Pakistani government and some are enemies.
Yes and no. The different tribes have a long history of infighting and turning coat, and the right to move towards armed confrontation is rooted in their pre-Islamic Pashtunwali (common) lawcode
But when a strong leader emerges the tribes/ groups rally behind him. Historically these where leaders like Ahmed Shah Durrani (founder of the Durrani Empire) and Sultan Mohammed Khan (founder of the original Islamic Emirate of Afghanistan)
Mullah Omar was such a strong and powerful leader. There wasn't any infighting under his command, and most of the internal opposition came from ideological differences. The TTP rallied around Baitullah Mehsud and later Hakeemullah Mehsud. Especially Hakeemullah was an exceptionally talented leader and commander.
When Fazlullah, who was much more incompetent, took over in 2013 things went south. Infighting (not with words but with guns) paralyzed the movement, the TTP crumbled, and they lost all their territory within 5 years. The lack of a serious bureaucracy means that any progress of inter-tribal ties usually gets lost whenever one of these competent leaders gets assassinated.
It's unclear where the current leader stands, and how much support he has gathered. The Gul Bahadur TTP faction is strong and in favor of talks with the Pakistani. The Haqqanis are equally powerful and have known links to the ISI. Any potentially unifying group will have to break their influence first.