So let's get this straight. You're experiencing things that everyone experiences in every house, but in your case you think it's a ghost. Let's go over that list of yours.
- Yes your house makes noise, because all buildings do. Buildings are constantly expanding and contracting, leaning and twisting, and slowly sinking into the ground on which they're built. The creaks and groans and even booms are called dynamic load distribution, and if a building didn't do that it would collapse very quickly. You'll even hear (and feel) creaks walk across floors and down walls, and it's totally normal. Nothing unusual there.
- Dogs & cats are presumed to react to ghosts, that's a very popular (yet never proven or disproven) theory. But while they MIGHT react to ghosts, they also DO react to other things. They have the ability to hear a squirrel running through the neighbour's yard or smell what's in a garbage can half a mile away, and they'll react to that even though you can't hear or smell anything. The only way to confirm that pets can see spirits is to ask them and wait for their answer, which has never been done.
- Before you blame a ghost for stealing your stuff and returning it in random locations, ask yourself why a ghost would do that. Then ask yourself if your memory is 100% accurate and photographic at all times, and be honest when you answer.
- If you ever find yourself in a building with no airflow whatsoever (as you assume your house to be with the cold spot), you're actually in a coffin. All houses are designed and built to have air moving through them all the time, so an occasional cold spot doesn't mean anything.
- No one has ever successfully captured a ghost. Even though I believe in ghosts (which I do), I've never seen a ghost-photo that doesn't look like it was faked. Fake photography has existed as long as real photography has, and ghost-pics are the easiest thing in the world to fake.
- You can't prove that ghosts exist to anybody, so don't bother trying. Like I said, I believe in ghosts and still wouldn't believe any proof that you showed me. The proof is just to ambiguous and inconsistent to be considered proof at all, because there are too many other possibilities that could have produced the same result in the picture / recording.
Finally, you haven't seen anything ghostly going on. You've seen stuff that might have possibly maybe been the result of a ghost, but you haven't seen any ghosts. In fact all the stuff you've experienced is stuff that people experience every day. And when something happens to everyone every day, it doesn't count as paranormal.