How did Minato teleport to the battlefield of the 4th Great Ninja War without being there already to set up the kunai?
I know he uses kunais and marked seals to teleport, but Minato was in Orochimaru's place. If he would throw a kunai by kunai to get there, I guess it would take too long to get to the battlefield.
How did the kunai get there that fast?
After reviving, Minato was eager to see Naruto and even sensed his chakra from Orochimaru place. From Fandom Wiki about Hashirama Senju
At the request of Sasuke Uchiha, Orochimaru releases the souls of the first four Hokage from the stomach of the Shinigami so that he can reincarnate them. After taking in their surroundings, the First and Second Hokage are excited to meet Minato, the Fourth, and take him as a sign of the village's prosperity. Minato says he does not know since he died before the Third Hokage did.
While Sasuke talks to the First Hokage, Minato detects Naruto's chakra and is glad to sense he has gained full control of the Nine-Tails. From Fandom Wiki about Minato Namikaze
Minato, eager to see Naruto, arrives first, just in time to warp away the Ten-Tails' Tailed Beast Ball, saving Naruto and the Allies.
Flying Thunder God Technique used by Minato is not limited to teleport using kunai marker. There are a lot of things more into it. Actually, it was a special attack created by Minato to mark a different location in the battle area by throwing a lot of kunai's to take full advantage of Flying Thunder God Technique in the battlefield.
The Flying Thunder God Technique is a space–time ninjutsu created by Tobirama Senju.
Before the Flying Thunder God Technique can be performed, users must first mark a target with their "technique formula". The formula is applied after the merest touch and cannot be removed; it will remain in place even after the user has died. There is seemingly no limit to how many targets can be marked with technique formulas, as Minato Namikaze routinely uses dozens at a time.
By entering a dimensional void, users can instantly teleport to a technique formula's location whenever they please, regardless of distance. To an onlooker, it may look like the Body Replacement Technique, but the Flying Thunder God actually has more in common with the Summoning Technique. Anything that the user is holding, contacting, or that is linked with their chakra will teleport with them, but this requires additional chakra (add: Minato has nine-tail chakra) to do; particularly large objects can require so much chakra as to place a limit on how far away the user is able to teleport Users can choose to teleport to a different location than the objects, or they can teleport objects without teleporting themselves.
Conclusion: there is no limit to how many locations that Minato can mark using the Flying Thunder God technique. Minato is very smart, and to take full advantage of the technique, I am sure he already marked his family members like Naruto using this technique so that he can teleport to them anytime. He also lived his life as the fastest shinobi, he already traveled around the world, I am sure he already marked a lot of long-distance locations where he traveled in his life before. Another possibility is Minato and Naruto's chakra is linked via nine-tail chakras, so the condition for the Flying Thunder God technique is met and Minato can teleport anytime to things connected with nine-tail.
