Hi friend! I see you've been around for a while, but nice to meet you anyway! I think I have some insight on this because I'm a HUGE fan of the "light atmosphere, dark undertone" thing, so hopefully my thoughts might prove helpful!
- What are your favourite examples of fiction with dark undertones, but a light atmosphere?
I had to think about this one for a second, but the first thing that popped into my head was Akiba Maid Wars--it's quite literally about maids working in maid cafes in Japan, but the maid cafes sort of function like Yakuza/mafia groups, so they're constantly mugging each other or getting into literal gun shootouts...you know, all while they're fronting as these cute, innocent maid girls. Definitely a harsh contrast there.
Something more subtle would definitely be Fruits Basket. This might come from a more visual sense, but I'd say this falls in the category. Not sure if you've ever seen/read it, but the gist is that this girl, Tohru, lost her mother and is basically homeless, and ends up being taken in by a family who are cursed to turn into animals from the Chinese zodiac when they get too emotional (I believe, it's been years since I've seen it). It's definitely your standard shojou anime in where the MC is very cute, very innocent, kind of naive, very sweet and nice, and the characters surrounding her are definitely very comedic and do their own thing. But as the show goes on, it starts to come out that everyone's dealing with their own shit, some more than others, and I recall it getting pretty dark as the final episodes rounded out.
Soul Eater is another one! Though again, might be a visual thing. Soul Eater follows a lot of demonology, mythology, and occult lore so that's already starting off pretty dark. But the characters, their interactions, the situations they get into, and the way they handle them definitely spin those normally dark things into something more aesthetically light. Granted, there are DEFINITELY moments of "holy shit this is fucked up" but they're greatly contrasted with "lol Black*Star is a fucking chimp" or somebody getting an aggressive nosebleed because they saw some cleavage.
- What are some good ways of hinting that a character's past wasn't exactly pleasant, beyond them saying so?
This comes down to the art of "showing, not telling." It can be as simple as having a character react to things a certain way, to physical things they might suffer with. For example:
-I'm writing an original character in my fic who was raised by his father, who was basically some more fucked up incarnation of Dr. Jekyl and Mr. Hyde, in which some days he was tolerable and other days he was a deranged menace. 30-something years later, said character now flinches involuntarily when people raise their voice at him, and he immediately tries to fight if people walk or run up behind him. Just long-term results of dealing with a genocidal maniac as a dad :>
-I'm writing Guzma in a more realistic take in my fic, and go about physically and mentally illustrating the fact he was abused by both his father and Lusamine in numerous ways. Physically, he wears a compression sleeve on his shoulder for burn scars caused by experimentation, and he has scars that he's hidden under tattoos from his dad's beatings. Mentally, he immediately reacts badly to parents yelling at/condescending their kids, his reaction to almost everything high stress is anger (granted, not in a violent way a lot of times), and he's very protective of his video game consoles and other electronics (because his dad used to smash them).
-In a webcomic I read (called 'Uriah' in case you're curious), there is a character who grew up mute. They're mute because as a baby, their mother was so overwhelmed by their incessant crying that she got high/drunk or whatever (I think, she might have also been sober and just tired) that she filled their bottle with boiling water and fed it to them, causing damage to their tongue and vocal cords, rendering them unable to speak upon becoming of age to be able to.
- How can "dark" characters contribute to a light hearted plot, without ignoring their dark past?
This can come down to characterization and generally how you "execute" it. Light-hearted plot doesn't mean it can't have its moments of "dark." Take Fruits Basket for example, the plot itself is very lighthearted, the characters tend to be very lighthearted and comic-relief-y, but they absolutely have their moments of angst and uh-oh. Ouran High School Host Club is another one I can think of where it's entirely made out to be a comedic anime but lo and behold, the last four or so episodes get pretty dramatic and start to delve into one of the characters more, and we find out his past/home life is pretty fucking dark.
Drawing from those examples, you can have the characters be like Kyo from Fruits Basket, in where they're the angry comic relief all the time while dropping hints here and there about WHY they're so angry. Or you can have them be like Tamaki from OHSHC, in where he's the dramatic leader of everything and gets hella worked up when his friends do shit without him, only to reveal he's like that because his family life blows.
My plot is by no means "light" so to speak, but I definitely have moments of "light" in where my characters, who have, in layman terms, been put through the fucking wringer, roll up and provide the comic relief while still shouldering their trauma from their past.
So all of this to say, think about how your characters deal with their baggage. If you're going a light-hearted route, you're probably not going to be delving too much into the weight they're shouldering
at the moment. Characters who have endured trauma, once healed, might spend their days doing whatever it is they like to do, and might just act as any other person would. However, some might put up emotional walls. Some might get irrationally angry at things. Some might try to make everything a joke. Some might be nervous around other people. Workshop how the post-trauma manifests for them as they go about their lives, and go from there.
- What are some good ways of coming up with plots that aren't too dark, but still have enough tension to be exciting?
Hmmm I might not be a good source of advice on this one because I think every time I've attempted to come up with a lighthearted plot, SOMETHING dark ends up manifesting within it. However, I have come up with stories within the stories that are entirely lighthearted and just deal with really lowkey or mundane things (though sometimes not!).
I'd say start with competition. Maybe plot something around characters fighting for a thing. It doesn't have to be anything major or life-defying, it could just be a race to fight a region Champion, or who can catch/evolve a Garchomp first. Journeyfics are pretty good with this.
Maybe you could also work around a mystery? Perhaps not anything dark like murder or people going missing, but maybe something more benign like Pokemon suddenly not able to use their moves, or a shortage/complete outage of healing items at the PokeCenters. Or maybe a certain place is getting ravaged by an invisible force, and it turns out to be some angry ghost-type? Idk, I feel like there's a lot of options there but I immediately want to make them all convoluted and edgy LOL
Anyway, I hope this all helps in some way! Feel free to respond or DM if you have any questions/concerns, and I'll see you around!