CW: nsfw, non-human anatomy, mentions of infertility, slight possessive behavior, otherwise that's pretty much all!
Malleus Draconia
Malleus does have a rut, though it's not exactly the same as what you would see in a beastperson's rut. (It is still called a "rut" or "rutting season" though.) It's largely based on external temperature over time. While he, himself is warm-blooded, many of his reptile ancestors were not. If the daytime temperatures warm to be rather balmy (90 °-100 ° Fahrenheit or around 32 °-38 ° Celsius) for over a week, it can be expected to trigger his rut, and he will remain in his rut for however long it takes before the temperature drops again. Due to the location of Briar Valley, that means his rut is rarely ever triggered in his homeland, far to the North. That, however, means the opposite is also true: the warmer a location he is in, the more likely he is to have his rut triggered and have it last for a long period.
Malleus is demisexual, so his sex drive also differs from the average dragon fae. Generally speaking, unless he is incredibly familiar and comfortable with a partner, he essentially won't have a sex drive at all. Of course his rut will make him want to mate, but he isn't likely to seek someone out for it unless there is someone he is already in a long-term relationship with.
Malleus has an increased olfactory sense which allows him to pick up changes in others bodies in line with pheromones and horomones. He will pick up on others ruts and heats but it won't really affect him. He might use it to tease a partner, though, if he notices the change in their scent.
To get a bit nitty gritty, since he is a dragon fae, Malleus is classified as a Squamata (i.e. scaled reptile). He has scales that are plate-like and he will periodically molt. (However, molting time for squamata fae varies-- typically they molt more often when they are younger and are growing quickly and then less often once they reach late adolescence and maturity. TL;DR Malleus molts but likely only once every few years.) This might seem like a lot of nonsense, but it's not without purpose: squamata also share another pretty common features that has to do with mating. They have hemipenes and hemiclitores, meaning that anatomically, Malleus has two dicks. Biologically, it serves the function of ensuring that he would be able to mate should he need to mate multiple times, but realistically it just means that he has two dicks and two separate refractory periods. Depending on his partner, this could be a good or a bad thing, just depending on their stamina. Unlike other reptiles, his anatomy doesn't fully retract into his body, only partially.
So far as the appearance of Malleus' dicks, they're similar in structure to a human's, though visibly different. It wouldn't be entirely incorrect to describe it as spiny, though the reality is less unpleasant than it sounds. His dicks are ridged until around halfway down the shaft from the head. So long as his partner is prepared (which they would be, if he has anything to say about it-- he cares about them too much to let them get hurt) it wouldn't hurt, though it would feel pretty different from a typical dick.
Malleus' rut is interesting, to put it one way. As silly as it might sound, like some of his reptile cousins, dragon fae mating is largely based on status. Since he is a prince, and there's not a whole lot he needs to do to maintain his status as prince, his rut largely consists of him just being extremely tired and wanting to laze around in bed all day. If he does have a partner who wants to spend his rut with him, it's going to be a lot of napping and cuddling interspersed between sex. In fact, he's so exhausted by it that he can hardly drag himself out of bed to eat, so being cared for would be much appreciated. (And when I say exhausted I mean he is out. Like snork mimimimi out.)
When he ruts, Malleus does get pretty territorial. He dislikes having people he doesn't actively trust anywhere near his room or his partner. He also will protect his partner bodily, and will usually place himself between them and someone else. This ALSO usually means just laying his body over them because he's so tired. He will apologize for squishing them after he gets his wits about him again.
Due to his biology, without some medical assistance he cannot have biological children with a partner that doesn't lay hard-shelled eggs. It's not impossible for him to have children with a human/beastman/merfolk partner, but it's not something that can be done without medical assistance via artificial insemination, and will likely require a third party to provide a "host egg" for them.
Sebek Zigvolt
Being half-human and half-nocturnal fae, Sebek doesn't experience all of the symptoms of a rut that most nocturnal fae of his species do. His 'ruts' are usually an increased libido in the wintertime, and otherwise a pretty regular sex-drive.
During his rut period, regardless of if he has a partner or not, he tends to get a bit more aggressive and combative than other times of year. This tends to be the time of year that he gets into spats with the people around him without meaning too. If he is in a relationship with someone, they're pretty much the only person not on his warpath. Well, and Malleus, but he's a special case considering Sebek is his guard.
Like Malleus, he has a good sense of smell-- better than an average human though not quite a strong as a full-blooded fae. He will usually be able to smell the change in a partner indicating a readiness to mate, however he likely won't be able to pinpoint what it is that he is smelling and will simply think they smell nice and it kind of makes him want to spend more time around them.
Sebek's dick is pretty normal looking in comparison to other kinds of fae. To be crude, the only real attribute that he has inherited from his Nocturnal Fae bloodline is that he's hung like a goddamned horse. That being said, I don't think he probably realizes that he's on the big side compared to most humans (he's never really paid much mind to it), so he will probably be quite smug if he is told that he is. Like most other humans, his anatomy does not retract into his body when not in use.
Sebek is a special case when it comes to producing offspring. While he is biologically compatible with both humans, beastpeople, some merfolks and other fae (of the non-egg laying variety), because of him being a hybridization of humans and fae, his fertility is quite low. If he and a partner would like to have children with each other, they will likely need to look into methods of assisted fertilization or will simply have to be exceedingly lucky.
Sebek's ruts are easy to miss if his partner is not in-the-know about them. His sex drive is a bit elevated, but not extremely so. As mentioned before, he gets a bit aggressive, though otherwise he's simply pretty lethargic and unusually touchy. If he has a partner, he will often want to be close to them, and he will nuzzle against their face and neck. It's a instinct that he doesn't realize that he has that is his way of signaling an interest in mating.
Most of Sebek's knowledge about sex and anatomy comes from standard human sex ed, as Lilia taught him and Silver at the same time. It's not wrong, perse, but definitely leaves him with some inexplicable things that are his fae biology that he's unaware of. He probably isn't even aware that he HAS ruts unless someone else points it out to him. His response would be a solid progression of "don't lie to me" to "wait that can HAPPEN?" to "Fae truly are amazing".
Lilia Vanrouge
So, while it's heavily implied that Lilia is a vampire, that's not entirely accurate. I won't go into the long winded spiel I would if I were just talking about headcanons about Lilia's species in itself, but I believe he's moreso a general parallel to an unseelie fae. There are fae that are shown to drink blood, but without knowing more about him in canon I'm not going to label his species at this time.
That being said, and not to be boring, but Lilia is essentially an exact parallel for humans and their mating behaviors! He doesn't have ruts, and he doesn't have an especially strong sense of scent that would make him key into someone else's ruts/heats either. (In fact, it's possible his sense of taste and smell might be a little either altered or dulled, considering what we see in canon...)
So, given all this, I'm sure most of you are wondering why the hell Lilia is even on this list, right? Well, Lilia (and the others, but especially Lilia) are implied to be capable of changing their appearance for short periods. While that's a taboo magic in canon, you can't tell me that Lilia wouldn't be down to fool around with some shapeshifting in the bedroom.
Lilia can reproduce with most humans, merfolk, beastpeople, or fae (who don't lay eggs). Or he could just... Yknow, adopt another child. He's cool with that, too...
However, even with the experience already raising Silver, he's definitely not always got the best paternal instincts. Chalk it up to a combination of being a vet and being used to raising... Some particularly durable babies (*cough* Malleus *cough*). He does his best and tries to do right by his kid(s?) but sometimes it simply doesn't go to plan despite his best intentions.
Hello flesh eater, I am that previous anons child. They died from Mafia that you sent (or at least that's what they said) and I am going to kill you however that not all first I'll kill your little roommate then I'll kill your food supplier then your that rei person since you seem to like it then I'll kill the rest of your pathetic allies and then finally you. Before I go just to remind you from what you shown us you are exactly like your dad anywho that is all for now until we meet again.
unborn anon child voice: i would have killed you're* friends... if i didn't die in a car crash