Ok, friendships can be complicated, especially as a demigod in this series. From what I can tell demigods usually have trouble fitting in with mortals because of their demigodness.
They've usually got ADHD and Dyslexia, tendencies from their godly parent, monster trouble from using phones and technology like that, and are usually are labelled as troublemaker by their school. These would probably make it hard to make friends.
For example of godly parental tendencies, Percy is reckless and rebellious resembling Poseidon and the untamed seas, Annabeth inherits her mother's wits and intelligence, Clarisse is very violent and warlike like her father Ares, Jason and Thalia are strict and mature like their father Zeus/Jupiter, Leo is crafty and creative and understands machines more than people like his dad Hephaestus, Nico is very dark and moody like his dad and enjoys spending time with the dead more than the living like his father Hades, and Connor and Travis Stoll are mischievous and cunning and like to play pranks and steal things like their dad Hermes.
Then there's the actually being a demigod. They're in danger from monsters, can't tell their friends what is actually happening and sometimes have to disappear for periods of time to deal with Demigod stuff, worry about the possible danger of them being close to their mortal friends, they have totally different life experiences (one lives an ordinary mortal life and the other fights/kills with monsters for their life), and they're physically different as a Demigod (generally faster, stronger, better reflexes, etc). It's hard to get close to people when you have to spend a lot of time at the Camp and you have so many differences and obstacles to being ordinary friends.
However, we
should still try to hang out with people and be social. Being social is an important part of life and even if we don't make close personal friends, we can still
train/improve our social skills and be likeable and get along with others, instead of just closing off and not associating with anyone who isn't our father or a plant. Plus, there's always the chance of finding other demigods. I mean, on one hand it's unlikely because what are the chances of us happening to be in similar age range and location to other demigods who then end up going to our specific school, but on the other hand we're a demigod and shouldn't be surprised if that sort of thing happens.
Now, onto a less social focus: what other powers that we might have a child of Demeter! There's the obvious
Chlorokinesis. But, reading through the series have sort of shown that while the demigods generally get a powers/ability from their godly parent, there are also other powers under their parent that they can train/use. Percy originally starts out with Hydrokinesis and ends up with various other powers that fit Poseidon's portfolio. Leo has the skill of builders and craftsmen and a talent as engineers are second to none. As part of this, he can instinctively detect, identify, and operate any piece of machinery. But, as the child of Hephaestus, he also has the ability of pyrokinesis.
Now, the way I look at it, there's several ways that I can see how some demigods have extra powers from their parents.
First off, one way is the demigod in question got lucky and got the right godly genes or such. Basically, they happened to get more or got lucky which godly genes and also got the extra abilities. Whether or not they can actually use it is up to the individual in question. Natural talent might let them break through/realize their ability (like Piper and her Charmspeaking, she just ended up using it with realizing it by just asking for stuff), or they could be pressured until they erupt in the ability, like Percy and his new-found ability to have a personal hurricane when fighting the Titan Hyperion in Central Park in the Battle of Manhattan.
Secondly, another way is that all the demigods have the ability to use those powers, but either lack the training to do so/or the natural talent to realize they can. Basically, most never realize they
could do so or don't have talent to naturally end up using it, without being pushed to the limits and making a breakthrough. For example, this way means Piper was basically had a really high natural talent at Charmspeaking, which let her use her instictively use her ability without having to be pushed into a corner and make a breakthough to get it. This also explains how Piper managed to Charmspeak such powerful entities, she was basically
really talented at at and since she ended up realize she had the ability when she was younger, she ended training/using it fairly often (espcecially during her adventures with the other demigods). Essentially, all the children of a godly parent have the abilities, but aren't individually talented enough to naturally use it and realize they have the ability. So, since they never realize they
could do it, they never try to/never break through in their ability to do so.
Thirdly, another way is that it requires a certain strength to use various abilities that they get from their godly parent. For example, Percy managed to manipulate the water in toilet when Clarisse tried to dunk his head in it fairly easy, but years later and much stronger, he still struggled a bit control the personal hurricane he used to fight Hyperion and found it tiring to keep going (from what I remember, so take with a grain of salt).
Forthly, is that they are granted the ability by their parents, though I find this unlikely. In this way, the godly parentslets them have the other abilites. However, I find this unlikely, because I feel they would give the abilties to far more of their children than the few that they do, and they wouldn't know to give certain demigods their ability so early (ie, Piper got her Charmspeaking when she was young, used it to ask for various things vs. Piper getting her Charmspeaking just before her first big quest because Aphrodite thought she would need it).
Fifthly, demigods gain their other abilities by fulfilling their role as the child of their godly parent (I also consider this unlikely, but fun to consider). This mean the more they do fitting their status as a Demigod, as a child of their Parent, and their 'story', the stronger they get/the more abilties. This sound fun and make sense in some parts, but it fails in others.
This is mostly from a novel I read, where individuals, after they died, by fulfilling other's belief in them gained power. It was Norse-based, but using an example of one guy, he claimed he was the son of Thor (in reality he was not), but he kept claiming it and during one fight a lightning bolt struck his weapon as he fought someone and killed his enemy while leaving him unharmed. That made his legend as "Thor's Son" grow and when he died he had some powers similar to Thor (and ended up in Thor's legion fighting monsters) and his legend as Thor's son grew even more and he gained more power.
This fits in some ways because as Percy continually proves himself, his 'legend' as Poseidon's child grows and he gets more powers and stronger. This fails in others, as in Piper being able to Charmspeak, despite no one knowing she's Aphrodite's child and with no legend so to speak.
That being said, whether or not we can get other abilities that Dememer has, is up to the QM.
Anyways, moving on from all that,
Demeter's Abilities are here. There's Chlorokinesis( with a subset in Taphokinesis), Geokinesis (possibly even more than Hades and Hera), Fertility Manipulation, Nourishment Manipulation (with a subset in Gluttony Inducement), Thermokinesis (with subsets of Atmokinesis and Season Control) Culinary Art (she's a good cook apparently? May not be relevant here), Cursing (historically, not really used in the series, turned a demigod into a gecko for ratting out Persephone), Transfiguration (she turned abunch of monsters into wheat in the Battle of Manhattan), and Ant Manipulation (historically, helped Psyche by sending ants to sort the seeds that were spilled, but possibility of some sort of animal manipulation or such?).
I think I may have gotten a bit too interested/excited, so take this all with a grain of salt. It's mainly ideas and possibilites, so it's in the QM's court in the end.
TL;DR: We should still be social/train our social prowess. There are multiple ways/reasons we could get/train into some of Demeter's abilites and Demeter does have some cool abilities. However, in the end the abilities are up to the QM whether they are possible or not or such.
Aren't monsters in PJO hidden from mundane sight? If so, I'm not sure if telling the teacher is going to work if they can't even see the thing.
Think they can still kinda be seen but only as odd people. Percy had a similar situation as a kid iirc and Tyson went to school for a while.
Yes, the Mist prevents people from seeing monsters or other stange events as what they are, instead changing to fully fit in with their worldview. So, they won't see him as a monster/rotting man, just an ordinary man. Still, we could just point out the strange man staring at kids to the adults, they should call the police and chase him off like what happened with Percy an the Cyclops at his elementary school.