Coin is the leader of the rebellion, the leader of the District that developed the bomb and the person who told a plane to fly there and drop it. If Gale hadn't developed this bomb, Coin would have dropped an ordinary one.
Before the Capitol battle, Gale had explained to Katniss his series of bombs designed to feed off human compassion: a small bomb would go off, and then when medical aid rushed in, a second bomb would go off, killing those people as well. Incidentally, it's this exact type of bomb that took Prim's life.
Katniss speculates that Coin deliberately sent Prim to die in the Capitol bombing in order to fully gain her trust, but it's never outright confirmed or denied.
Nobody was sure exactly who was responsible for the the bombing or even the exact timeline. Due to its dilapidated condition, the Capitol Arena was not considered a high security area, so anyone could have sneaked in at any time since the 9th Hunger Games and planted the bombs without anyone noticing.
Snow laughs after Katniss killed Coin because he enjoys the irony of the situation. He avoided the official execution ceremony, even though Panem's citizens still take their revenge on him, while Katniss ends up snatching away the victory and power that Coin thinks she has successfully secured.
Coin killed Prim to destroy Katniss because, as Boggs (Mahershala Ali) explains before his death, Katniss is her biggest threat to maintaining her power over Panem because of the influence Katniss has over the people.
Still, it was because Coin was revealed to be a ruthless leader with her own political interests. President Coin manipulated the rebellion for her own gain, willing to let people die to achieve her goals while portraying herself as a hero against President Snow's cruel government.
Katniss's focus on survival and her family's safety prevented her from fully considering romance, but her feelings for Peeta and Gale diverged in the end. Katniss ultimately chose Peeta because he understood her trauma and she didn't want to lose him, proving her love for him.
The double bomb that kills Katniss Everdeen's sister, Primrose, was designed by two rebels: Beetee and Gale, Katniss's lifelong friend. Previously, Gale had explained that the double bombs are designed to appeal to mankind's weakness for compassion.
In the end, Katniss and Gale grew apart, as many childhood friends and young loves do. She needed something different in her life, and with Gale's link to Primrose's death, Katniss found a reason to cut ties. If Katniss ever wanted to find comfort again, she knew she had to return to Peeta for the long term.
If the gun wasn't invented, those people wouldn't have died in that manner, so yes the inventor still was indirectly involved with those people's deaths. Conclusion: Yes, Gale was indirectly involved with Prim's death, as in if he didn't create the bomb then she wouldn't have died.
Even if Gale didn't intend to murder Prim specifically, he certainly intended to murder somebody. The two-phase bombs that he and Beetee invented were very clearly made with the intent of targeting medics and other civilians trying to save those wounded during the first phase of bombing.
She asks Gale and his family to escape into the woods with her. He agrees happily, and confesses that he loves her. He is disappointed by her reply that she cannot love anyone romantically at such a perilous time. He is further angered when he finds out that Katniss plans to bring Peeta along into the woods.
Snow can't stand to see a young woman betray a young man's affection—his view of what happened 65 years ago. And so he takes out his old, festering wound on Katniss.
According to the star behind Effie, Elizabeth Banks, she and Haymitch's Woody Harrelson improvised the scene. Considering she's been adamant about the characters having some romantic connection, it only makes sense that they'd share a goodbye kiss. It's very on-brand for Effie, as well.
Essentially, Katniss was afraid that if she was to kill President Snow, then the whole revolution fails, and the rivalry would still continue. Therefore, Katniss had to sacrifice by killing Coin in order to end war, and knew that Coin couldn't do anything better than Snow to save the Panem.
It is likely that he is a relative of Hilarius Heavensbee. In the Mockingjay - Part 2, Plutarch appears to smile as he looks at Coin's dead body, suggesting that he approved of her death.
By killing President Coin, Katniss risked her safety in order to not only avenge Prim's death but also gift the people in Panem a chance to live in a peaceful and fair country for everyone. Katniss was incarcerated for a time, and she was sent back to District 12 after she was deemed unsuitable for a trial.
She remembers that they did indeed promise not to lie to each other anymore, and she realizes that Snow wasn't lying to her about Coin's role in the parachute bombing. He has no reason to lie to Katniss. His death is certain, but the future of the Capitol is not.
This suggests that Katniss loves Peeta, and not just because she feels that she owes him her life. Instead, Katniss wants to protect him and bring him home because she has strong feelings for him, even though she isn't sure what those feelings mean.
Katniss is at first so angry with Peeta for his comments, believing that he made her look weak, that when they get off on floor 12, she shoves him. He knocks an urn over, shattering it, and then falls and cuts his hands on the shards.
He is portrayed as a villain, but his ultimate goal is to maintain peace and stability in Panem. Snow recognizes the threat of rebellion and the potential for chaos if the districts were to gain too much power.
