I'll list some notable details about the clan first;
1. One of four noble clans of Konoha
2. Considered the strongest among the four (I mean the Uchiha are dead, Akimichi only focus on eating potato chips, and Aburame are weird insect folks. No wonder the Hyuga are leading)
3. The Hyuga are descends of the Otsutsuki clan, from Hamura's side to be specific, making them distant relatives to other clans like Uchiha (wow!), Uzumaki (does that mean Sasuke and Naruto are cousins? Holy Alabama)
4. They still have (or had during first part of Naruto) this weird obsession with hierarchy and thus the clan is split into head and branch houses, with branch shinobis always in risk of being Avada Kadabra'd by their blood cousins (essentially).
5. Hamura's direct descendants can also potentially acquire the Tenseigan without facing the adverse effects, unlike the branch house members, though that is clearly incredibly rare in the first place. This means a Hyuga has the ability to possess more than one KG.
6. The main focus here is the Byakugan, one of the three great dojutsu. It is a magic eye that gives pseudo omni-directional vision, ability to see through solid objects, track better than naked eye and most importantly, view the chakra system of other people.
Gentle fist is the fighting style developed using the advantages of the Byakugan, where Hyugas use their innate ability to expel chakra from every chakra hole in their body. This requires immense chakra control and training but results in an ability that can have pin-point accuracy when dealing with the weak points of techniques/or even people. All of its fighting forms includes either palm attacks, or finger attacks, or chakra blasts. Forcing your own chakra into someone else's chakra system essentially results in devastating damage - making them fierce opponents, moreso at close range. This fighting style is also known to be the strongest style of Taijutsu in Konoha, even though it trades in an individual's raw power for precision. These fast gentle strikes are ruthlessly strong yet versatile.
For the final question, I only have one answer: Nara rules U_U