My story is set in a magical world hidden within our own, and it has many magical version of things we do.
So was Sabrina the Teenage Witch (comics debut 1962), Men In Black (comics debut 1990), and Hellboy (Comics 1993). Rowling doesn't have a lock on hidden underground societies.
It has wands but I have decided to change it and make it that there is a ritual to make your own wand. There are also brooms but I was going to have it so witches and warlocks have to make their own.
Like Bedknobs and Broomsticks (Based on Books that debuted in 1943)?
I am going to make a magical government, a council with branches and departments, that cover different things.
I am going to create a wise old man, to act as the mentor for my story, but pretty much every fantasy series has a wise mentor character. LotR - Gandalf, Narnia - Aslan, HP - Dumbledore, etc.
Last I checked, Aslan wasn't an old Man... This is a standard character archtype for the Hero's journey... It's as old as storytelling and can trace back to cultures and societies that never interacted with each other and had no plausible means to do so.
For the first part of the story my main character is going to be in a weakened state and her followers are working to revive her.
I don't recall this as part of Harry Potter.
I am also going to make magical shops. I am not going to create an alley, but I am going to create shops hidden in secret places.
Again... older than dirt... real life examples would include various speak-easies set up during prohibition (Hidden Bars and Pubs that had front businesses to mask the comings and goings of clients).
I am going to give witches and warlocks the power to turn into animals, but I am also going to give them other changes as well.
Prominently used in fairy tales and children's tales. Witches turning people into toads was all the rage back in the day if the fairy tales are to be believed.
I am going to have some spells and potions that do the same as in Harry Potter, but I am not going to copy unique ones like expect patronum. I am going with ones I know are alright to use. I am also going to create my own unique potions and magic that do things not in Harry Potter.
Again... Harry Potter did not invent magic or potions.
I am going to have paper communication, letters, newspapers and posters, because they are more fitting for magical world. I am going to invent of different way of mail transportation.
The rest of the world relied on paper to communicate for millennia
I am going to create food that does magical things.
Again, nothing new... we'd have to look to fairy tales and myths of old to find the original stories that had this.
I am also going to create items that do funny things, because I want my story to be very dramatic, with a chunk of humour mixed in.
Yeah... that's not a thing Rowling has a lock on.
My story is going to be set in the 90's because all the tech stuff we have today doesn't really work for magic.
This is the second time this week someone said the 1990s were tech scarce. Take it from someone who grew up at this time... we had cellphones... we had the internet... and computers... The "Dot Com Bubble Burst" happened in the early 2000s because we were so obsessed with making websites to sell things so you didn't have to go to the stores! And don't you dare forget the Beeper!
That said, one of the things not discussed about Harry Potter is that if you didn't go read stuff on the website, you couldn't tell it was set in the 90s (The films used 2000s-2010s fashion choices and the books never gave any dates). It's probably part of why it had staying power. Go read animorphs, for a series that didn't age well because it was hella-full of 90s references (they tried to rerelease them in the 2010s by removing very dated 90s pop culture references... and realized there wouldn't be much book left without them.).
That all said, if you want to do a throwback to a long gone decade... I mean... I don't want to think of the 90s in the same light as I thought of the 60s or 70s while growing up in the 90s... but time stops for no man, and I've yet to see a good "set in the 90s" series... mostly because the 80s was way cooler.
I am going to set it in the UK because all the old fashioned buildings we have here are fitting for magic.
Have you been to the UK? Or watched Top Gear? Perhaps you may have been unaware of this historical thing called "World War II" and "The Blitz?" London (as with most of Europe) had to do some extensive rebuilding following that and most buildings are not much older than late 40s to 50s. You can find old buildings in the country side, but that's not a UK exclusive thing.
I am going to give them in old fashioned clothes and robes. For example, pin striped and tweed suits, bowler hat and old cardigans and sweaters.
Why? Your book is about teenagers... why do they have to wear old clothes that make them stick out when you said there's a hidden world (Disney's Sorceres Apprentice... the live action one... actually did have a reason for this... but it was confined to shoes and the two older Wizards were frozen in stasis in their old man clothing... their younger apprentices wore modern day clothing).
I am also going to have one character's family be carers of magical beasts, because I am very adamant about animal welfare and I wanted to show that in my story.
Never happened in Harry Potter... I would suggest maybe a farmer angle.
The key differences in my book are:
There is no magical school, because that instantly makes it compared to Harry Potter.
Harry Potter didn't do this first... just did it famous... that said, more common than not, magical schools aren't a thing in fantasy. Most children in developed countries do not go to boarding schools. The only other "Magic School" I can think of off the top of my head is Hexside (Owlhouse) which was based more on a U.S. public high school than then a boarding school (It's similarities with Hogwarts were more to poke fun at the school. Like how Hexside used to use a "Choosey Hat")
The magical names I am going to use are witches and warlocks
Not a Rowling thing. The term "Warlock" is used in Harry Potter, but it seems like an archaic term for Wizard. In modern literature, "Warlock" is actually a term that is being moved away from, as it means "Oath Breaker", which not only is a negative... but also implies a demonic barter for magic power, which most heroic magic users types move away from... don't want the original Harry Potter is Satanic crowd messing with you.
My main villain is a woman, and I am thinking of using the soul jar trope with her, or is that too much like Harry Potter?
By "Soul Jar" do you mean remove your soul from your body so you can't die? Thats... close... It's not something Rowling invented. It's been found in myths and fairy tales... but it might be too close for comfort and best to look for other means. If this means something else (the term is used in DND as a type of spell with some unusual mechanics... but nothing like Horcruxes in Harry Potter).
There is a main trio but their powers and stories are all very different from Harry Potter.
The "Trio of heroes" is not unknown and quite common. It's used a lot because the characters can become an Id, Ego, Superego personality dynamic (Logical Thinker, Decisive Thinker, Emotional Thinker OR Spock, Kirk, Bones). It also works because a group of 3 is the smallest amount of people that can have a disagreement where one of the members is in the minority of opinion. Almost every high school sitcom and drama has the "hero" and his/her two friends (almost always one friend is the opposite gender of the hero) and none of the trio are romantically interested in one another (that doesn't mean they can't date... or be attracted... they just rarely make a lasting relationship beyond BFFs and they are cool with it. This also allows a secondary trio to come in through their romantic partners. See Buffy the Vampire Slayer. Almost everyone outside of Giles came into "The Scoobies" because they were dating Buffy, Willow, or Xander.
There are going to be merpeople but I am going to make them, more human than in Goblet of Fire.
Mermaids predate even Hans Christian Anderson's most famous work, "The Little Mermaid."
My main group are going to be teenagers, not kids, when they start.
JK Rowling didn't invent teen or kid heroes (And her characters were teens for 5 of the 7 books... and Harry is the youngest of the trio and only one who was 12 at the end of book 2.).
TL;DR: From your 30,000 feet up look at your story, there's nothing wrong and J.K. Rowling didn't create everything in her book whole cloth. Lots of things are taken from British Myth and Folktales.