The following is my best theory currently for how the events in Episode 1 (the first anime arc) of Umineko no Naku Koro ni were committed. However, I offer no motives or exact logistics.
Kanon is the murderer, and he is in cahoots with Nanjo.
– Kanon bribed Nanjo with money, because the Ushiromiya servants are very well-paid. They earn enough money that they can simply retire after a relatively short period of employment (possibly just a few years) and live out the rest of their lives in comfort.
– Kanon gave the letter to Maria in the garden. He was wearing a Beatrice costume. He looked feminine enough for the role and fooled Maria.
– Kanon put some drug into six of the cups of tea or coffee that the adults wanted during their late-night family discussions. It did not matter who drank the poisoned cups; it was random. Gohda and Shannon taste-tested the stuff and both of them were unfortunate enough to have picked the drugged ones.
– Kanon transported those six people to the shed and killed them. Maybe he used that wheelbarrow from earlier.
– For the chained room, when Genji left to fetch Natsuhi and Kanon was to get Kumasawa, he was alone and had the opportunity to kill Eva and Hideyoshi. Perhaps the chain was just duct taped onto the door frame or wall. After killing the couple, Kanon then got Kumasawa and the chain-cutter.
– Similar idea: Eva and Hideyoshi were already dead when Genji and Kanon tried to open the door. Kanon just killed them earlier in the day and duct taped the chain, etc.
– Then again though, I could be very, very wrong if it has been said in red that the door chain was never removed from the wall.
– Kanon faked his death. Nanjo declared him ‘dead’.
– Nanjo could’ve placed the letter on the table in the study room. He might have reached across the table for something (that tin of mackerel?) and allowed the letter to slip out from the sleeve of his roomy lab coat. Or, the letter had been there from the start, hidden underneath a book on the table, and Nanjo moved the book.
– Kanon got back into his Beatrice getup and Nanjo let him into the room. Kanon fooled Maria again, and killed Kumasawa and Genji. Then he betrayed Nanjo and killed him, too.
– Natsuhi and Kanon fired simultaneously. Kanon had a long-range (sniper?) gun that put him out of Natsuhi’s Winchester’s range, so he was safe from her.
– Battler, George, Jessica, and Maria saw Kanon, who was still in his Beatrice costume in the dark. Kanon shot the four cousins with his long-range gun.
– Kanon died. In what method, I don’t care too much, but I hope it’s not some cheesy reason, like revenge or he was under orders from Kinzo and he killed himself since he reached the goal of killing everyone else, or he accidentally killed himself in celebration, or that he became so mentally insane he committed suicide.
A demo of how the Eva/Hideyoshi room could’ve been locked:
(Pretend that the wall end of the chain has already been broken off the wall, and the door end is already in the door slot)