How Can Pianists look at the Sheets they are Playing without looking at the keyboard? Have they memorized them?

Yes, they look at the music rather than the keys because they know where the keys are without looking--sorta the way I type. Once your finger knows that this key is there, then you don't have to watch it press the key. It will come with practice--a lot of beginners put stickers on the keyboard so they can see where C and all the other notes are, but they don't need them after a month. Your little organ will be fine for learning on--if you get good enough that you want lessons or better sound quality you can go for a piano later or find one you can borrow every now and then.

One more thing--once a musician is familiar with a piece of music, they begin to recognize patterns--they see that a combination of notes begins in a certain place, and that the next note is a step higher on the staff and the next note is ... and wind up just seeing and recognizing the whole pattern. In other words, once they have practiced a song for a while, they are seeing and playing a series of notes, rather than reading and recognizing one note at at time. With a couple years of practice you may get good enough that you could sight-read and play something you have never seen before at the speed you can read it, but don't expect that to come quickly--it comes over time as you start to recognize that when you see this, you need these keys.

For me, it basically gets down to muscle memory. After practicing a piece of music enough times, you just get a better feel of where the next hand placement should be. It's the same thing with guitar. That's why some guitarists can even play the instrument behind their head.

On either instrument, you don't have to focus on each hand independantly once you get used to the timing. It's the same way people can sing and play at the same time; if you learned them independantly of each other you may need to do a bit of relearning / practice to remember how to make them work together but it really just gets down to practice.

In regards to reading music, it's really the same thing. Practice helps you to recognize certain chords. Even then, if you get a new piece of music it may take a little time and practice to make sure you've got it worked out correctly. A good piano teacher can help you learn the basics more quickly, and then you can run with it from there.

Of course. I can type anything without looking at the keyboard.

The same way you can walk without looking at your feet. You know your way across the keys without having to look down.

Same as people who touch type don't look at the keyboard, they only look at the screen.

Practice and practice again.