Question regarding piano music (playing & composing)

[uptick]

Piano has long been considered to be one of the deep arts when it comes to music. As a person who is planning on embarking on this long and wonderful journey, I had a thought that's been bothering me a bit - now this is mostly due to my lack of knowledge and experience in piano and music in general, but nonetheless, I hope someone more experienced could help shed some light on the subject.

I've been whistling ever since I could remember- hearing a random song and capturing the rhythm and melody and improvising on the spot based off of what I hear. Now, when it comes to most instruments, whether it's harmonica, violin, trumpet, saxophone, guitar, most of these instruments' sounds are very singular in nature (singular as in the player only plays either the rhythm or the player plays the lead). An exception of this is i think some forms of fingerpicking guitar styles like that of Tommy Emmanuel in which he makes his playing sounds like he's playing both the lead and the rhythm a the same time.

Anyway, the point i'm trying to make is that with most instruments, there's only that one sound, one rhythm or melody to worry about. And when there's both lead and rhythm, these are usually done by two players separately, or in the case of music composing, one would perhaps create the rhythm part with chords first and then use it to inspire and set the tone for the leading melody (in guitar for example).

Now, music making/playing this way is probably how most get accustomed to music. And having been whistling for so long, I can totally see the process of playing and creating music in such a simple form as I've only have to worry about that one SOUND at a time so coming up with an idea for music is simply taking that one sound in my head and transferring to the instrument.

However, with piano, it's often not as simple as right hand being the lead and left hand being the rhythm/bass, in reality, both hands aren't seen as separate entities but one single instrument - just sometimes playing poly-rhythmically. As someone new, this is completely foreign to me as it's completely foreign from all the other instruments where you just have to worry about one sound at a time.

My questions is, how does one go about hearing 2 sounds at once in your head when trying to come up with a musical idea? Do you hear 2 sounds at once or is this a fallacy? Is this something that comes naturally with time and training? or is this simply a deeper musical instrument that requires more theories/musical structures and as such, its process is less based on intuitive feelings and improvisation and feelings, but more on the science of it all (knowing the theories, how to layer the 2 sounds and interweave them together, etc.

[indianajo]

Learning music is in part by doing.  Just training the ear is part of the process.
While my years of piano lessons allowed me to play up to 8 notes at time without straining, it was very much a black spots on the page fed to fingers on the keys process. Not any involvement with the jukebox of the brain, which ran and learned songs  quite independently of the piano lessons. 
I didn't start learning chord structure until I studied a "teach yourself guitar in 6 weeks" book.  Guitar is all chords at fist.  I had chord theory as a piano student, but it didn't include any listening.  I was all black spots on paper associated with certain names.
Now I'm beginning to hear chord structure of songs, and the guitar induced skill is begining to fit my piano/organ hands, which I am must more skilled at anyway.  I'm starting to begin to play by ear, in my sixth decade.  Who said old dogs can't learn new trick?
So try it, you'll like it I'm sure.  The more you do the more you can do. 

[pianoplunker]

However, with piano, it's often not as simple as right hand being the lead and left hand being the rhythm/bass, in reality, both hands aren't seen as separate entities but one single instrument - just sometimes playing poly-rhythmically. As someone new, this is completely foreign to me as it's completely foreign from all the other instruments where you just have to worry about one sound at a time.

My questions is, how does one go about hearing 2 sounds at once in your head when trying to come up with a musical idea? Do you hear 2 sounds at once or is this a fallacy? Is this something that comes naturally with time and training? or is this simply a deeper musical instrument that requires more theories/musical structures and as such, its process is less based on intuitive feelings and improvisation and feelings, but more on the science of it all (knowing the theories, how to layer the 2 sounds and interweave them together, etc.

Not sure what you mean by "2 sounds" but I can tell you that music theory does not change because of the instrument. There is no special theory for piano.  there are definately methods but not theories. I have known Sax players, drummers, and of course Geetar players who knew the same theory just as well as anyone else.  You are on the right track of understanding that piano is linear.  You might be over-complicating the theory requirement though.