My short answers, and then I have to run.
1. The nature of who we are points towards the existence of mind/intelligence/spirit - call it what you will, but our ability to think, act, grow, change, our free will - we are not merely mechanical robots... the universe is made up of more than matter and energy - there is also information, laws, forces, and life/intelligences/spirits. I view our spirit as being the animating force of our life and thoughts, and do not believe that our own spirits are the only ones that exist within the universe. As with all things, there are lesser spirits, and greater spirits - the greatest of which, is God.
We're not robots because we can think, learn, and make choices. So can other intelligent life forms such as dogs. I'd like to know how you know that there are spirits, and different classes of them no less.
2. Spiritual experiences. I believe in God because He has spoken to me through His Spirit - literally. He has strengthened me when I needed it, and guided me through tough decisions. There are different forms that spiritual communication takes, but I believe that everyone has a conscience - everyone has that little proverbial jiminy cricket on their shoulder guilt tripping them into doing what is right - I think we all really do have angels sitting on our shoulders, and sometimes devils too.
By spoken to you, I'm assuming you're not referring to an audible voice but rather a gut feeling of what he wants you to do. The human conscience is called the holy spirit when people believe it's god rather than their own mind. When it's something "good" it's the holy spirit, and when it's something "bad" it's the devil.
A mentally healthy person's conscience from what I can tell is for the most part based on compassion for others and an understanding of how actions affects them. Consider the following scenario:
You go to a friend's house wearing a red shirt, and everything seems normal. As you leave, someone tells you that a person at the house has an emotional breakdown when seeing the color red. You feel guilty. Next time you're invited, you might remember and take special care not to wear red. This is because if you remember (you might forget and wear red anyway), chances are you'll have sympathy for the person and anticipate the negative reaction from wearing red. If your caring about the person and your reputation outweigh any reason you would have for wearing red, you'll probably wear a different color. This is a logical, rational mental processes that requires no supernatural explanation including the holy spirit.
There's another scenario that's both applicable to the holy spirit and testable. If someone is saved and said to be guided by the holy spirit, then the holy spirit should be able to offer divine inspiration instead of being limited by a physical brain. Let's say that this person hasn't completely read the bible yet and eats a big plate of shrimp lo mein without having any reason to feel guilty. This person then finds out that eating shellfish is a sin; I know it's Mosaic Law, so maybe the person was one of those the law was directed at. The person will begin to feel guilty, because being told that something is wrong makes you feel guilty when doing it. If it was the holy spirit, the feeling of guilt shouldn't be limited by the knowledge of it being a sin. Likewise, if the command doesn't apply to the person but he feels guilt from thinking it's a sin, it's the same process of the mind's natural conscience rather than a divine cosmic force.