Is it possible to own both a dog and a cat, at the same time, in the same house?

Absolutely. People do it all the time. There are 5 cats in my house and I dog sit. Obviously I only take dogs that do good with cats but many dogs do and the cats don't care about the dogs. 

Yes, but you must be careful to have a “low predatory instinct” breed like a Rough Collie, to be safest in feline coexistence. Certain breeds of dog, particularly the majority of hunting breeds and most Spitz breeds, no matter how socialized, are safe around cats entirely. For some it is as tempting to tear a cat to pieces as prey as it is for cats to mess with a birdcage in the room. It’s not worth the risk to the life of your cat.

Having a dog and cat that peacefully coexist under the same roof is possible, but it does require a bit of a time commitment. There's no guarantee your cat and dog will get along with each other, but gradually introducing them and giving both of your animals equal amounts of attention can help.

Of course it is. One of my team leaders in work has a dog and a cat (funnily enough one of the guys on my department got his cat from her neighbour. He like me doesn't like dogs though). You just need to make sure the dog and the cat get along and don't attack each other.

Yes, that is possible for some dogs and cats if they get along. Many people have both.

Of course it is possible....I own 2 dogs and a cat.all animals will live together and be alright if you bring them up to do so

Why not - millions do.   At one point we had a couple of feral kittens with our small pack.   My previous neighbour had 3 cats with her 3 Whippets (yes Whippets) too.

I have 2 cats and a dog currently. They are not the best of friends, but they tolerate each other. No epic horrible fights, no killing each other, just harmonious tolerance.