You have to travel from New York city to Los Angeles you cannot disappear in New York and appear in Los Angeles!! Or be in both cities at the same time.

This is a quantum superposition, or called a 'complex probability wave function'. It does not mean you are in New York and appear in LA or that you are in both cities at the same time.

What it does mean is that the way the Schrodinger equations work is that the superposition or probability wave function is simply the SUM of all possible states, that sums to 1 (100%).

So say you have two possible states, either asleep or awake, however I don't know if you are either asleep or awake, so I assign a probability of 50% chance you are asleep and a 50% chance you are awake. There is a 100% chance that you are either asleep or awake.

As I have not observed what state you are in, I can only say you are in a quantum superposition and there is a probability function (a wave, in this case a square wave).

Just because I do not know if you are awake or asleep that does not mean you are therefore both awake and asleep at the same time, or that there is one world where you are awake and another where you are asleep.

It just means that as I have not observed you, makes no difference about what state you are actually in.

But for my math I can assume you are in one or the other (with a probability).

Once I observe you and I find out if you are awake or asleep then the wave function collapses and the probability of you being the state that you are in is 100% (or 1).

It's nothing magical or bizarre.

(Schrodinger's cat's name is Heisenberg)

And quantum entanglement faster than the speed of light!!

Nothing is faster than light.

Quantum entanglement is this: You are 1 light hour away from me, I order a pair of shoes from a store I get the store to send one shoe to you and one to me.

We don't know whether we have the left shoe or the right shoe.

You are 1 light hour from me and you get your box with a shoe in it, the instant you open your box and see that the shoe you got was the left shoe, you know that the shoe in my box in the right one, conversely the instant I open my box and see a right shoe I know the shoe in your box is the left one. I get that information faster than the speed of light (I get it instantly). But that information got to you (and me) at or below the speed of light.

Of course, before either of us opens our box you can say the shoe's are in a quantum superposition and are both left and right in a complex probability wave function, which collapses once either one of us observes the particle (shoe) by opening the box.

(side note: the entire Schrodinger's cat thing was proposed to expose the absurdity of the model, as opposed to what actually happens)