The four characters to look to answer these questions would be Gene, Phineas, Brinker, and Leper. Gene, Phineas and Leper are round and dynamic while Brinker is flat and static. The first three are round because Knowles gives the reader descriptions of their mannerisms, personal agendas, goals, triumphs and disasters; whereas Brinker is flat because he is important to the movement of the narration, but his personal feelings and thoughts aren't delineated. Next, Gene, Phineas, and Leper are dynamic because all three go through life-changing experiences that change their minds and/or personalities from what they believed at the beginning of the story. Brinker, on the other hand, is static because his beliefs never change; he is the same at the beginning and end of the story.
Below are quotes that help to show an example of each character's development:
Gene: Round and Dynamic
"I never killed anybody and I never developed an intense level of hatred for the enemy. Because my war ended before I ever put on a uniform; I was on active duty all my time at school; I killed my enemy there" (204).
The above quote shows Gene after he has changed. He gave up his rivalry with Phineas and learned that the problems he was having that year in school were deep inside himself.
Phineas: Round and Dynamic
"I'll hate it everywhere if I'm not in this war! Why do you think I kept saying there wasn't any war all winter? I was going to keep on saying it until two seconds after I got a letter from Ottawa or Chungking or some place saying, 'Yes, you can enlist with us.' . . . Then there would have been a war" (190).
This quote is Phineas admitting his denial of the war for the whole winter because of his broken leg. He has just suffered another break to the same leg and must face the fact that he may never enter the war, now.
Leper: Round and Dynamic
"A Section Eight discharge is for the nuts in the service, the psychos, the Funny Farm candidates. . . They give you a Section Eight discharge, like a dishonorable discharge only worse. You can't get a job after that. . . You're screwed for life, that's what a Section Eight discharge means" (144).
From the beginning of the book, readers are shown a gentle, introverted and intellectual Leper. He is innocent and safe behind Devon walls; but once he enlists in the army, he goes crazy and AWOL (absent without leave). This quote shows the intense situation Leper finds himself in after his innocent view on the world is lost forever.
Brinker: Flat and Static
"Brinker looked the standard preparatory school article in his gray gabardine suit with square, hand-sewn-looking jacket pockets, a conservative necktie, and dark brown cordovan shoes. His face was all straight lines. . . and he carried his six feet of height straight as well. He looked but happened not to be athletic, being too busy with politics, arrangements, and offices" (87).
Brinker is flat because his inner emotions, dreams and motivations aren't deeply explored. The reader gets the basic outline of his character, but not many details. He also remains the same straight-laced guy throughout the whole story because he doesn't go through any dynamic changes.
The term "character development" often relates to how the character changes through the chronological sequences of the narrative: how the character develops in relation to events and experiences. You seem to be asking more about "characterization": characterization is how characters are introduced and presented.
In brief, the two main characters Phineas (Finny) and the narrator, Gene, are given full (rounded) characters having a broad range of thoughts, emotions and psychological motivations and reactions. The secondary characters are presented with less detail and, in some sequences, like the opening of the book, are mere shadows that are there with them but given flesh and reality, though is not true for all sequences.
"Is this the one they jump from?"
None of us knew.