Cockatiels are smaller pets, so you will need to watch that your other or existing pets do not harm your cockatiel when you move it into your home.
Cats on the other hand are natural preditors, and are more likely to look at your cockatiel as their next meal. They will tend to lurk and wait for the cockatiel to be removed from the cage before attempting to catch it. Some will even be so bold as to climb onto the cage and attempt to reach it through the mesh. Although this may not cause direct harm, it will upset your cockatiel, which may injure itself by flapping around its cage.
A tame bird is especially vulnerable to a cat, as its natural fear is lessened. Try to keep your cockatiel in a room that your cats aren’t allowed into, and if letting your cockatiel out of his cage, first check that the cats aren’t around. Never be tempted to leave the bird unsupervised in the room, even for a short time, especially if you have children. They could open a door and let the cat in by accident, which could well spell the end of your bird.
Open fish tanks can present another hazard for your cockatiel. If the bird falls into the tank, its plumage will become saturated, which will cause it to sink and drown. To avoid an accident, make sure the fish tank has a cover over it at all times.
If you own a parrot or bird of another species, you will need to introduce them very slowly. Your pet parrot could be jealous and attack your cockatiel. Your established bird may object loudly when you are working with your new cockatiel, and also attempt to bite his feet through the meshing if the cockatiel lands on his cage. If the cages are placed close together, the established bird may also try to bite the cockatiel through the cage bars.
In order to reduce conflict, try to spend more time with your established bird. Try letting both birds out together, and this may reduce aggressiveness, and in time they may form a close bond, perhaps even roosting side by side in the same cage.
There is no risk of a cockatiel cross breeding with another bird species. They have never in history been successfully cross bred with any other species, as they are so different to the other bird species.