Welcome to the community! Fuzzy looks like to be a very adorable and healthy little Cockatiel, and is definitely young, I'd say 5-6 months is pretty accurate...
With Cockatiels you sometimes cannot tell the gender just by looking at them, sometimes you can, it depends on the mutation...But at only 5-6 months old you definitely cannot tell the gender, only after their first big molt (around a year old) will it be possible to tell Fuzzy's gender...You can't see it in the photos you posted, but if you look at the underside of Fuzzy's tail-feathers and right beneath Fuzzy's vent, you'll probably see some white/yellow striping...If Fuzzy keeps that striping after the first big molt that Fuzzy goes through, then Fuzzy is a female...If after Fuzzy molts those stripes/markings on the underside of his tail go away, then Fuzzy is a male...But you'll have to wait until Fuzzy goes through that first big molt, which usually happens when they are between 8-12 months old...Otherwise, you can always take Fuzzy to any Avian Vet and have a blood-test done to determine the gender, which you sometimes have to do anyway depending on the mutation...Or there are labs online that you can actually have test for gender through the mail by simply plucking a few of Fuzzy's fresh chest feathers out, and then you send them to the lab in the test-kit they send you once you order it...You order the test kit, they send it to you, you pluck a couple fresh chest feathers and send them in to the lab, and in a couple of weeks you'll know his gender...
You should ALWAYS do at least a 30-day quarantine whenever you bring home a new bird, regardless of where the new bird came from or whether it was around other birds...The 30-day quarantine should be done in an entirely different room than your other birds, and ideally behind a closed door...Once the 30 days is up and assuming Fuzzy is not showing any signs of illness, then you can locate his cage in the same room as your other birds, though you need to introduce them to each other outside of their cages very slowly, only under supervision, and you must be prepared for them to not get along or to even be aggressive towards each other...So they may or may not be able to be out of their cages together or not, you'll not know until you introduce them and they spend some time with their cages in the same room together after Fuzzy's 30-day quarantine...
As far as the proper diet for a Cockatiel, it's not any different than your other birds really...Yes, a main staple-diet of pellets is much healthier than a seed-mix staple diet, but if you can choose a healthy, low-fat seed-mix that contains NO sunflower seeds, NO nuts of any kind, and NO dried or cracked corn kernels, then it's much better for Fuzzy's health and will help to prevent Fuzzy from developing Fatty Liver Disease over time....There are many low-fat, healthy seed-mixes available online and in pet shops, you just have to read the ingredients and look for ones that say that they are "Sunflower Free", a lot actually say this right on the front of the packaging, then look for a sunflower free mix that also has no nuts (specifically peanuts, they are not good for your birds), and no corn kernels or cracked corn...And once you get Fuzzy eating a healthy, low-fat seed-mix, then you can start to slowly transition him over to a pellet staple diet...If you go to the Harrison's Bird Food website, they have a wonderful "Seed to Pellet Transition" plan that you can print-out and follow that usually works very, very well to switch them over from seeds to pellets...
As far as fresh veggies, Cockatiels eat all of the same fresh veggies that other parrots do, all of the dark, leafy Greens, and then pretty much all fresh veggies except for Onions and Leeks, which are toxic to birds...Other than Onions and Leeks, most all fresh veggies and dark, leafy greens are fine, it's just a matter of trying different fresh Greens and Veggies and finding out which ones Fuzzy likes. He should have a bowl of his staple diet (either a seed-mix of pellets) in his cage at all times, and then should also get a nice big serving of fresh veggies and/or dark, leafy greens every single day.
As far as fresh Fruit goes, it should not be given every single day like the fresh veggies and greens are, because all Fruit contains a very high sugar content, and in captive/pet birds that aren't flying 10 miles or more a day, that extra sugar from fresh Fruit gets turned into fat that is stored in their livers, just like the fat from the sunflower seeds, the nuts, etc. So you should only give your bird fresh Fruit 3-4 times a week at most, as an added supplement or treat to his regular staple seeds and his fresh veggies...And pretty much all fresh Fruit is okay EXCEPT for Avocados, which are toxic to birds, and then you should also avoid giving your birds any Citrus Fruit, such as oranges, grapefruit, lemons, limes, etc., and also Tomatoes, because they are extremely high in Vitamin C, which greatly enhances a bird's absorption of Iron from the rest of their food,
and birds cannot absorb much Iron at all, because over time they can develop "Iron Storage Disease/Syndrome", which can eventually cause your bird to become extremely sick and cause them to die years to decades before they should...However, there is no need to feed your birds Citrus Fruits or Avocado when there are so many other safe, healthy fresh Fruits you can give them as a treat, such as apples, bananas, strawberries, raspberries, blueberries, blackberries, seedless grapes, mango, guava, kiwi (remove the seeds), passion fruit, star fruit, coconut (in small quantities due to sugar content), pears, etc...Again, it's just about finding out which fresh fruit Fuzzy likes...
Other occasional treats can include sunflower seeds, nuts, and then other foods such as "people food" occasionally...If you can figure out what is Fuzzy's favorite treat, then that's the treat you want to save to be Fuzzy's "Training Treat", as Fuzzy will be more willing to work for his favorites...
I'm glad you've got toys on their way for Fuzzy, since he's going to be in quarantine by himself for the next month he needs lots of toys and foraging activities to keep himself entertained and his mind stimulated...He looks like a perfectly healthy, adorable little baby Cockatiel!
A female normal grey will have more of a grey face (like yours does) If I guessed right now,I'd say you have a female..BUT to be positively sure,you need to wait until the first molt,OR you can bring him/her to a CAV and have a DNA done..honestly,I would wait for the molt...its a lot cheaper!
Imagine doing that to Rio I would def have some fingers missing 
And it looks like Fuzzy was starting to like her too..
