Fictional characters are good for character studies due to knowing their inner thoughts. There's no debate about why they do the things they do, because the author tells us. We can then judge these characters. The judgment can be matched against real-world behaviour (as opposed to the reverse), and we can be confident the judgment still applies. The predictions will remain valid.
Han De is supposed to be paranoid.
Weiheng Hui is supposed to be a coward, and says so.
Richmond Rain Stroudwater is actually a coward. A rather high-fidelity rendition, no less.
I would say the key feature of a coward is feeling terrified if they're not perfectly safe. If anything could conceivably be trying to kill them, they assume it is trying to kill them. They're paranoid and self-absorbed.
Han De's paranoid ends up looking like good preparation - indeed, he wasn't paranoid enough, and survived due to dumb luck / author fiat. It doesn't count if they're really out to get you. He should just tell his family he's a calamity attractor, as it turns out this attracts calamities. He could convince them to stop being one of the calamities he's attracted.
Hui isn't a coward at all. He simply fails to enjoy fighting as much as he's "supposed" to. In his case, being pressured into unnecessary fighting is what a coward would suffer - he bravely refuses if possible.
There's nothing cowardly about being afraid of fearsome things. Poking a tiger with a stick is stupidity, not bravery. Failing to be afraid of the fearsome makes you weak and/or dead. If something is likely to hurt you, being afraid of it is merely good sense.
A true coward like Rain isn't merely fearful. They are not only afraid of the many things that can damage their soft, vulnerable bodies. Their cowardice is crippling. Their cowardice makes them even weaker than they otherwise would be. They panic over nothing. They flee from their own shadow.
They're even scared of looking at themselves. They can't know themselves, and therefore must quite rationally fear the result of every conflict.
This makes them more violent than the courageous. Since everything is trying to kill them, it's fine to try to kill it back, right? Cowards are, if not dangerous exactly, certainly hazardous. You're minding your own business, they construe it as a threat, and snap at you. Hazardous waste.
They're too scared to admit they're a coward. They fearfully refuse to look at things, and thus end up full of cope and seethe. "I'm not scared of you!" (They're paralyzed with terror.) "Anyone would be scared of this!" (Even someone genuinely threatened by it isn't that scared.) Cowards have to violently condemn anyone who makes them scared, to avoid condemning themselves. (It doesn't work, but that doesn't stop them.) Cowards are too scared to resist peer pressure and end up violating the few virtuous principles they have. Cowards are too scared to look into another's mind, lest they start understanding their own by analogy. The only person they sympathize with is someone being terrorized, because it gives them an excuse to try to child-proof the entire world. "Fear is the only issue! I'm going to ensure nobody needs to be afraid ever again!" Ambitious, in a sense. They want a world with no lions no tigers no bears. Oh my.
Cowardice works a lot like the ur-sin, Pride. Instead of trying to destroying everything glorious to avoid being outshone, they try to destroy everything glorious because they're afraid it's going to kill them.
Cowards are highly recognizable because they have to say anything which makes them afraid, which is anything more threatening than a kitten, is morally reprehensible. They end up lionizing kitteh and doge and snek because they've declared everything else abhorrent.
Saying they're scaredy-cats is an insult to cats. Felines are indeed skittish, but everything they run from is plausibly a threat. They don't startle at nothing. They can also learn a thing is safe, instead of packing up and trying to shred everything that scares them. Cats don't respond to fear by making it their life goal to terrorize the world. Admittedly the way some cats toy with their food is reminiscent of the way a coward with an advantage will try to stretch things out as long as possible - often long enough to turn the tables on them.
As per usual, even other cowards are disgusted by cowards. Which is why Rain is a Mary Sue: rather than 'accidentally' accumulating all the local elites, as happens in SenescentSoul's mind, he would have been universally panned, even by folk he tried to be useful to. Which is correct: cowards are children. If you try to rely on them, whatever you're resting on them will fall when they're spooked and run off. It's only worth taking care of them if you're their mom or dad, because they're not productive.
Moms who are themselves cowards won't even defend their children. They talk a big game about going mama bear and won't willingly suffer so much as a hangnail for their kids' sake.
It's possible cowards only feel two emotions: fear and relief from fear. They like cats because kitties make them think they don't have to be afraid. Any nearby predator will take the cat before it takes them. If you make the feel perfectly safe, they don't finally have space to feel other emotions. When they're done feeling relief they feel nothing but empty.
Rain likes math because he doesn't have to be afraid of getting the wrong answer. As long as he doesn't screw up the arithmetic, he can be certain the answer is right. He can feasibly eliminate risk; that's what math is to him. Programming too. With suitably limited ambition, it's possible to write a bugless program, and a bugless program is, to his perception, perfect.
Are all the pop references about cowardice too? If you're caught or called out for using awkward, cringe lines, you can blame the other writer. With enough popularity you can be all, "No, it's the children who are wrong. I don't have be afraid of saying something stupid."
Rain gets his bell run by Lavarro. He's rightly afraid of Lavarro, who is erratic at best. He then starts behaving as if a Lavarro is going to jump out of random bushes at him.
The injury is partially his own fault. She wanted him to take off the helmet to see his face. He took it as an Absolute Command to not wear a helmet, too afraid of offending her to even think of putting it back on. His cowardice was the only reason he was in danger in the first place.
He ended up fine. If the Lavarro situation repeated, she would force him to take off the helmet again. Insisting on wearing the cap is doubly pointless. He's too afraid to notice either of these things. The coward is too afraid of fear to think clearly. If you are not a coward, then fear is not the mind-killer.
Subconsciously, Rain understands what threatens him most is his own cowardice. That's why he insists on the helmet; like a safety blanket, a charm to ward off his own fear. It doesn't work, because he's too scared to face the true root cause.
P.S. Lately age-related-decaySoul seems to have conveniently half-forgotten Rain is supposed to be a coward. That's character development, right? When the author forgets their character's vices? Maybe Rain isn't a Mary Sue. Maybe the other characters had the keen insight to recognize and predict the author's impending dementia. At least it's not a full MLP-style personality transplant. ("Character growth is when you suddenly become a completely different person due to failing one time.")