yes/no wrote:questions
1) Red feathers are powers yes? there are 7 dragon powers and red side has 6 of them, dragon fist/punch is nagi family side and is not included. Does that mean Nagi is not a red feather family? Makiko is the head of Nagi family so what family is souhaku head of?
No. There are 8 Dragon Gates: Spirit, Metal, Wood, Wind, Fire, Water, Earth and The 8th Gate.
The 8th Gate in itself is subdivided into 6 major power: Dragon Eye, Dragon Fist, etc. One for each Red Family.
Each of those 6 families has several vassal families. Each of them too has a minor power, coming from the 8th Dragon Gate: Dragon Pupil, Dragon Claw, Dragon Roar, and so on.
Nagi Clan is one of the 6 Red Families, he has both the Dragon Fist, which is a 8th Dragon Gate variation of his family, AND an Earth Gate, which is a regular gate available to everyone with enough practice.
Makiko is the head of Nagi Clan. Souhaku is the head of Kago Clan. His full name is Kago Souhaku Jyouun.
2) Madoka said F was established 8 years ago when most of the dragon gates were awakening to follow Mitsuomi, but how is that possible when most of them are younger than Mitsuomi?
No, that is not correct. The powers of the F were awakened 8 years ago, just as Shin's Dragon Eye. The did not come together as F untill some time later on.
3) F are white feather family or red feather? How come some of them have dragon gate when only red have them? Ishiyumi is red feather right? Is his water dragon bullet attac, one of the 7 powers or is it an elemental?
F are the heirs of the 5 White Families: Ishiyumi, Kabuto, Tsumuji, Kagiroi Mawari (the 6th White Family Heir is so far hidden from us).
White Families specialize in weapons and hand-to-hand combat, but as everyone else, they can access the 7 "normal" Dragon Gates. Ishiyumi's gate is Water, it is NOT the 8th gate that is reserved to the Red Families.
Additionaly, some of the F are of mixed blood, like Tsumuji Mataza, whose mother was one of the minor Red vassal families. He inherited his 8th Dragon Gate, Dragon Claw, from her.
All elemental attacks are also part of the regular 7 Dragon Gates. Electricity is a power coming from the Earth Gate (Souichiro and Fu Chi'en both use it), while Aya and Tessen can use the Water Gate.
4) Did the guy Mataza. one with 8 arms and spears die?
No, he is still alive. Just recuperating together with Makiko and his father in the forest retreat.
5) From the diagram of the dragon gates, there are 7 of them that run down through the middle from the head - crouch, 5 inbetween are elemental and the outer ones are something else. Are these the Dragon gates that grant them the fist/palm/eye/claw/leg/roar powers? If so shouldn't some of those gates be near the arms and legs? And do the elements have anything to do with the powers?
They are all elemental - spirit and metal are considered elements in the Chinese system.
As for the fist/eye/etc. - they are coming from the 8th gate that is reserved to Red Families and their vassals. There are major and minor powers coming from the 8th gate. Founding families like Nagi and Natsume get the major powers. Vassal families like Enmi get the minor powers.
6) What was the point of Ishiyumi as a F when hes so loyal to Mitsuomi? What was the point of reviving Fu Chien? And what was the point of bringing back Asshat into the Dojo? He's quite useless and way weaker than the rest, he's not going to do much and hes not funny, alien kid is at least smart.
Ishiyumi was sent to school to spy on Mitsuomi, thus he became closer with him, eventually switching his allegiance from Souhaku to Mitsuomi.
Fu Chi'en was revived because he had powers and Kago didn't want to trip his own hand by revealing his soldiers - Kagiroi and Kabuto beforehand.
Asshat was brought back because Maya needed 6 people to compete in the Tournament. Asshat was just handy and a friendly face. And anyway, Mitsuomi pretty much subverted or destroyed other powerful people in the school, so Maya didn't have many people to choose from.
7) How does Souhaku have more power than Dougen when he rules of him? Why didn't Souhaku give himself enhancements for more powers like Kagiro or instead of Kagiro himself?
Dougen is a Takayanagi and an old man, anyway. Apart from his knowledge, Dougen doesn't have much personal strenght anymore.
Souhaku, on the other hand, is the head of one of the Red Families and possesses and Dragon Gate.
As for the Kagiroi, I think that Souhaku didn't want to go mad by having so many Dragon Gates inside. Also, Kagiroi was a test subject. And Souhaku seems to be quite powerful on his own, without Makiko's eye.
I hope this settles your questions.