1) Discovering a fursona can fall into two different categories: you choose them cause they're cool or you choose them because the animal is associated with a trait that resonates with you. I don't know what other initiations could possibly take place aside from redesigning or rethinking what your fursona actually is. People constantly change and, as such, a fursona must change if they are intended as a reflection of the person.
2) Please, please, PLEASE if you are turning in this paper to professor or something then I beg of you to quote these lines: "
Rawr x3 nuzzles how are you pounces on you you're so warm o3o notices you have a bulge o: someone's happy

nuzzles your necky wecky~ murr~ hehehe rubbies your bulgy wolgy you're so big

ooo rubbies more on your bulgy wolgy it doesn't stop growing ·///· kisses you and lickies your necky daddy likies (; nuzzles wuzzles I hope daddy really likes $: wiggles butt and squirms I want to see your big daddy meat~ wiggles butt I have a little itch o3o wags tail can you please get my itch~ puts paws on your chest nyea~ its a seven inch itch rubs your chest can you help me pwease squirms pwetty pwease sad face I need to be punished runs paws down your chest and bites lip like I need to be punished really good~ paws on your bulge as I lick my lips I'm getting thirsty. I can go for some milk unbuttons your pants as my eyes glow you smell so musky :v licks shaft mmmm~"
5) The aesthetic in terms of furry art in the West has evolved ever since the 1950's. Check out Down The Rabbit Hole's video on furries for a more detailed info but basically the furry aesthetic started off very cartoony and inspired by early Disney Entertainment but eventually was refined while still maintaining a western-cartoony look. I'd also recommend you to do some research on Japanese furries since their overall aesthetic in regards to furry is extremely different to ours.
Here's a video of the bad copypasta, lol. So you can get a feel of what it would sound like to say this aloud. anyway.
1. My fursona's a Deer, because one time I watched Bambi and never got over it. That's it, that's literally the only reason, I just think Deer are cute. There is no initiation or whatever, there's nothing official about this community, it's so large and wide spread that the only thing some furries have in common is liking Anthropomorphic animals (Animals that walk on two legs) And even then, there are furries who don't even like animals when they're drawn that way, they prefer animals that walk on all fours or naturally.
2. "OwO, What's this?"- this is a shitpost, it means nothing but to make someone else cringe horribly. It is a phrase people use to make fun of Furry roleplay, something that can be extremely odd and embarrassing to read to people who don't partake in it.
"X3" Is supposed to look like a face. It's an emoticon, basically. It's the same as :3, which is also a face. These emoticons sort of originated from what is known as "Kaomoji's" which are those cute Japanese emoticons you see sometimes like ¯\_(ツ)_/¯ except they all directly reference animals. When someone goes :3 they're making an emoticon that's supposed to look like a cat, or a dog, or anything with a muzzle really. x3 is an animal with a muzzle that's smiling, but that also has it's eyes closed.
*Pounces on you*- Furry's roleplay with asterisks, and this is how they differentiate between what they're saying and what they're doing to someone else in text-based roleplay.
5. There's no particular "style" though the most obvious is fursuits. Fursuits, unknown to a lot of non-furries, have many different styles, however. For example:
Here's the western style of Fursuit, the one that most people see and recognize as "furry". It's also the one used the most here in the states.
and here's what's called Kemono Style, the style of fursuit that's often found in Japan:
There's also a lot of differentiation between fursona's in digital and traditional artwork. Some furries like "feral" animals, basically animals that walk naturally. While others are prone to "Anthros" furries that walk on two legs. And there's even some distinction between how you draw the legs and arms of these furry characters.
Digitigrade legs are when you draw the Fursona with legs that look more akin to real animal anatomy. Whereas Plantigrade is when the furry has legs that are structured more like a human.
If you would like a more visual representation of a character with these kinds of legs, Disney has already done it. In the movie "Robin Hood", all the animals have Plantigrade style legs:
Whereas in "Zootopia" all the animals have "Digitigrade" legs:
Anyway, I hope this helps. I personally have been in the furry fandom for about 2 years (according to the creation of this account lol).