King really should have listened to Ban's version of what happened, yes. You don't go and kill (petrify, whatever) one of your closest comrades because of what people claims he's done. But Ban never really denied killing Elaine, and he did do time for it so it would make sense for King to believe that he killed Elaine. Still, once again, he jumped the gun.
All King did was hit Gowther, which he honestly kinda deserved. He doesn't hate Gowther anymore and regrets how he acted towards him, they're actually friends for the first time ever.
What King did to Meliodas was reasonable, and justified. Meliodas has lied almost everything, how any of the Sins sans Merlin still believe in him is beyond me. Meliodas can't even tell the truth when his caught barehanded, like during the Kingdom Revolt Ban straight up asked him if he was a demon, which he saw and Meliodas still felt the need to change the subject to avoid telling the truth. Meliodas could also have told them about Galan's decree, he didn't and Merlin was trapped in the plot hole for God knows how long. He lies about things he doesn't even need to lie about, like if he knew Gowther was a doll. Don't go screaming "ELIZABETH'S MEMORIES!!" he could have just freaking said he knew the maker and that he was his friend, and that would be that.
If one of the most evil forces in history attacked you, your family and your friends, and you found out that your friend, captain and superior was a part of this force in the past, wouldn't you be the slightest bit worried? Especially if that person is lying, shady and untrustworthy? I like Meliodas a lot but not a lot of the decisions he's made.
I'm not saying that the Sins should sit around the campfire and tell their life stories, I get why Meliodas wouldn't want to speak about anything he's been through, but his constant lying and secrets really makes me wonder how anyone can trust him.
I am sorry but King wasn't far from being reasonable because he attacked Meliodas based on the fact that he was
a demon and that is all. He realized and admitted that himself in the flashback arc, he just exposed his true intention behind that attack and he felt really bad about it.
If Meliodas said that he was a Demon to Ban or King from the very beginning, then their friendship wouldn't even have existed in the first place, Ban and King would see Meliodas as the same monster that killed Elaine and the Fairy King forest. Demons are still entities which are see as evils and disgusting by any races throughout the history of NNT after the Holy War, and that disgust was taught generations after generations. Meliodas know that horrible fact, that is why he hides his identity and race from people and doesn't scream: " Hey, guys, you know what? I am a Demon, in fact, I am the son of the Demon King himself, how you feel about me now? "
If he said any hint about the 10C, creatures that existed in Goddess Elizabeth time, the chance that she will recover her memories is above 50%, a risk that Meliodas can't take, and yes, Elizabeth is ALWAYS with him, putting her away will just increase her natural curiosity and you know that Elizabeth get what she wants when she is curious about her lover, Meliodas.
Also, any hint of them will make questions like this inevitable: " By the way Captain, how do you know this? Aren't those demons from 3000 years? How do you know this? Give us something that makes sense, please. We aren't kids. "
Meliodas will basically shot himself and anyway due to their weakness ( at the time ) compared to the Demons, knowing their decrees wouldn't change a damn thing. For Merlin, it wasn't a problem because Meliodas knew her natural resistance towards decree, even his own little brother know it so Meliodas? Lol, you get my point.
Same for the Gowther thing, if he said that he knew Gowther's creator, several questions about how he knew, will come and if he keeps silent about it, they will suspect him even more, that is an endless loop.
If he said the truth at that time, that wouldn't benefit Gowther ( in fact, he wanted to forget anything related to his past ) at the time and not even himself, in fact, it would annoy him with more questions from his friends.
Elizabeth needs to know that Meliodas is a Demon and that he existed more than just a lifespan of a Human being to question herself, which risk triggering her memories, a risk that Meliodas was trying to dodge, remember, for him, Elizabeth is everything and the rest is just secondary.
That includes any hint or possibility for her to question herself or the situation, Meliodas want her to stay ignorant in each incarnation.