BEAUTIFUL BIRD!!
You always want to start off with their current diet. I am not sure about the Sunburst mix long-term. I know they do eat seeds more than some birds but sunflower seeds are like crack so if you can, I would look for a seed mix with less filler (avoiding corn, sunflower seeds, fruit chunks (because he is a parakeet) and peanuts---because they can harbor a fungus). If your bird is eating the pellets, make sure the seeds aren't fortified, as you could easily overdo the vitamins.
Zupreme isn't bad, but it isn't great (it's still considered a solid pellet--just not IDEAL). My bird is picky so its what she eats, but it has added sugar and colors (so it is kind of like the Flintstones vitamin of the pellet world--- long-term, you may look at something more natural like Tops or Harrisons)...But--Zupreem is considered reputable..Granted, I don't personally own a parakeet currently. I do know they can handle less sugar than a larger bird (and they still need to be careful).
Daily veg=important but very little fruit. One grape to a parakeet is like 300 to a human (or something like that lol).
No avocado, chocolate, xylitol, artificial sweeteners, caffeine, coffee (even decaf), no rhubarb, tomato, mushroom...avoid dairy unless extreme moderation is used (lactose intolerant). Avoid salt, sugar and preservatives...garlic, onions, leeks, chives, shallots etc =all bad for birds. When cutting up a fruit (say, apples) cut far from the seeds--same goes for pits. Parsley is controversial in some circles...You don't want to overdo spinach or dark greens and be careful with too much vitamin C--- it can lead to iron storage syndrome (for my cockatoo, vet said 1-2 Cutie slices per week, but not more).
No carbonation, no fortified human foods (e.g., most cereals, some pasta, some juices etc). No honey--especially raw (not just because of the sugar, but also due to botulism risk).
NO SHARING FOOD W/HUMAN SPIT IN IT--- eating off forks that have been licked or plates with double-dipping poses a hazard to your bird (despite the fact that a lot of people do this).
Your cat's saliva and bacteria in his nails/poop pose a huge threat--- even a playful swat can infect a bird with a bacteria that they carry and it is bad. The injury is often less serious than the infection that follows, so I would keep them FAR apart, even if he is the sweetest cat ever.
