Well, in fanfiction, there could be several reasons. It could be that Nico is suffering from some sort of after - effect of a battle. Maybe he was exposed to a harmful spell during combat and now his body is trying to expel the negative energy. Another possibility is that he's feeling homesick for the underworld in a way that his body rebels against the surface world, causing him to feel ill and throw up. Or perhaps he's caught a strange disease that is affecting demigods, and the first symptom is vomiting. And, of course, there could be some sort of emotional turmoil related to his relationship with Will that is so intense it makes him physically sick.
There might not be a whole lot of fanfiction specifically focused on 'Nico throws up' within the Solangelo context. However, if you dig deeper into the Solangelo tag on fanfiction sites, you may find some stories where Nico experiences some sort of distress that could potentially lead to such a situation. For example, a story where he's been poisoned or is extremely ill due to some magical affliction. But it's really going to take some time to sift through the available works.
Well, one possible plot could be that the other characters in the Solangelo universe are super confused at first. Percy might be all like 'Whoa, a baby Nico?'. They'd have to figure out how to take care of him. Maybe Will is the most determined to find a way to turn him back and in the process, there are some really cute and funny moments like baby Nico trying to grab Will's stethoscope and put it in his mouth.
Definitely Percy. He's always getting into wacky situations himself, and having a baby Nico around would just add to the chaos. He might try to teach baby Nico how to sword - fight with a toy sword, and it would be this really goofy scene with Percy making big, exaggerated moves and baby Nico just giggling.
Percy might tease Nico and Will a bit about it in a friendly way. But overall, it wouldn't change his relationship with them. He knows that the fanfiction is just the fans' imagination and not a true reflection of their real - life relationships. He would still be their friend and support them in their real adventures.
It could be for the sake of realism. In a magical world full of danger and adventure like Harry Potter's, characters are bound to get sick or have physical reactions. Hermione is a very studious and often overworked character, so it's not far - fetched to imagine her pushing herself too hard and getting ill.
Some fanfictions might depict Hermione throwing up from stress. In the world of Harry Potter, she often takes on a lot of pressure, like studying for exams, dealing with the threat of Voldemort, etc. A story could focus on how this stress finally gets to her physically and she throws up. You can use search filters on fanfiction websites to narrow down the results.
First, other teachers or staff members should help the teacher to a quiet and clean place, like the school infirmary if there is one. This allows the teacher to rest and recover.
Well, Nico and Percy are the main ones. Nico, who might have his own motives and backstory for standing up for Percy. He could be driven by friendship, loyalty or a sense of justice. Percy, on the other hand, is the recipient of Nico's support. There could be side characters too. Maybe Annabeth, Percy's girlfriend, who could be involved in the situation in some way, either supporting Nico's stand or being part of the conflict that Percy is in.
In this fanfiction, perhaps Percy has an idea or a way of doing things that is not accepted by the majority. Nico, who understands Percy better than others, stands up for him. It could also be related to a conflict with a particular group or character. For example, if there's a new powerful enemy who is targeting Percy, Nico would not let that happen and shows his loyalty by standing up for Percy.