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Thereza :
Hello, I've had budgies in the past and currently have 2, a female and a male. :) I just cleared my photos on my phone though so I'll have to post them later, sorry. D:
Budgies, or any other bird, are not any easier to take care of than let's say, a cat or dog. They're different, but they all need companionship, proper space and stimulation in form of entertainment. The only difference with a bigger bird is that they'll need less cage and room space, and their needs for entertainment might be simpler, as they're not as destructive.
Budgies are from Australia, meaning they can handle the heat far more easily than the cold. So if you live in a really cold area, please keep in mind you'll have to heat up their room during winter! Respiratory infections due to cold and hypothermia are very common issues with birds, especially smaller ones that can lose heat so easily!
The fumes thing is correct. Essential oil difunser, fumes from cooking with teflon, air fresheners and incense are all bad for, well, basically any pet, but especially birds! It's really recommended you use none of these things in whatever room the birds are hanging out in.
Budgies are energetic little things, and thrive best with other birds, especially males, so you should definitively consider having more than one budgie together. Taking care for 2 birds means a bigger cage, more toys, and you'll have to keep a bigger eye to see if either of them are becoming sick. Besides that, it's no different from taking care of 1, granted, of course, that they don't fight. Females tend to be far more cranky than the males from my experience (regardless of the other bird's sex, my female chases my male out when he tries to court her), and males tend to be very friendly regardless of sex, or sometimes, even species. My male budgie even tries to court my cockatiels, haha. So if you get a pair, as a poster above said, it's best to get 2 males. You also avoid the possible egg issues on a female.
I keep my birds out of their cages at all times except when I'm out of the house and at night, but they are hand-tamed. It'd be far harder to herd back a budgie that isn't human-friendly, especially if the wings aren't clipped, and that's why most people keep such birds inside their cage. I don't recommend it though, parrots are curious creatures, and will get bored of being in their cage all the time.
Most of the things that should be kept away from birds are related to air pollution, but also if they are to free-roam, keep in mind to keep away anything they could try to chew on that's hazardous for them (because they WILL try to chew on it) and any strings or, if you have long hair, clean the room they're in often because strands of hair and strings can tangle on their feet and cause issues.
Budgies' diet is around 60% seeds, 40% fresh fruit/vegetables. Poster above posted some good links on what to feed and not to feed. As a side note, you can also plant some of the seeds and feed them the sprouts. It'll be more nutricious for them than the seed alone. All you need is a small pot, some decent soil, sun and to water them every now and then. :) It takes them a week or two to sprout.
I had a dog around my birds before, but she was raised since young with other pets, and was the exception, not the rule. All mammals, including humans, have bacteria in their mouths that can be harmful in the long run for birds, so I wouldn't allow close contact that'd let the dog lick the bird. Unless you're sure the dog won't accidentally hurt the bird and the bird isn't afraid of the dog, I wouldn't really risk it.
Cats shouldn't be allowed near any small animals, period. They have gram-negative bacteria in their mouth that can possibly kill your bird, rodent or lizard, even if they're just grooming them with their tongue.
Birds do not need shots. Unless it's an emergency situation, shots on small birds are frowned upon as it places a lot of stress on such small animal. That said, you can do an annual check up your bird's health, and you can de-bug them every few months. I don't know the prices of vet bills where you are at, unfortunately, but if you're from USA, I've heard exotic vets can run quite expensive, so you would need to keep some hundreds saved in case of an emergency.
As an ending note, if you are from USA,
this website might prove useful, as it offers you a neat little test and breakdown on most common parrot species, and also can direct you to sources where to buy bird necessities (on that note, try to buy perches appropriate for your budgies' size, otherwise they might get bumblefoot!), what's the avian vet closest to you, and even tells you if there's any birds near you up for adoption. I'd recommend looking into adopting some budgies, since there's an unfortunate lot of unwanted parrots waiting for good homes. They're also cheaper than just buying a brand new animal from the store, with the adoption fees being around 10 to 30 USD for budgies from what I saw.
Hope this was helpful!
Blue // they/he 
