What are your views on how Everything came to be?
Everything came to be because God wants to be loved, so from him emitted Individual Souls who takes up various forms and manifestation with unlimited independence and shower love and service unto him in the Spiritual Universe. Not in this Material Universe.
Do you think Matter and Space have always existed? Or did one come before the Other? Or were they both created at the same time?
No Matter and Space are temporary, they are the creation of the Lord's material energy. There is something which is non-material that exist beyond space and matter.
Was anything "before" the Universe? Will anything be "after" it? Or do you see it as infinite?
Yes there is this place call the Spiritual Universe, within that, there are unlimited amount of Vaikunata planets(Spiritual planets). The material atmosphere which came later on consists of millions of material universes and we are in just in one of those millions of universes.
Where does the Big Bang fit into your beliefs?
Just imagine a frog living its whole life in the well and describing the ocean from within the well, similarly the Scientist are just frogs who assume this and assume that.
And if you believe a higher power created the universe, Why do you think it chose to do so? I'm not as interested in How the creation was accomplished, but Why...what motivated the deity to make the cosmos and the laws (or lack thereof) that govern it? (And of course, how did the Deity you believe in come to exist?)
Just imagine a Government who wants to build a place, it always reserved a place to build a prision because there would be those people who would always do otherwise, that is why a Prison is necessary to teach and correct them, so similary due to our misuse of independence we fall into the Material Universe which is like a Prison. This universe is a place for us to learn, experience and know that it is a place of misery. this place is not for enjoyment, if it is so we would be entangled here.
Why did the Souls falls from the spiritual plane ?? We are like little Gods trying to dominate each other, we want to enjoy by ourself and lord over nature without God, since we have unlimited independence to think for ourself we may think otherwise. So because of independence, sometimes we become a fool, independence means we can do whatever we want, So like this many of us fall into the Prison(Material Universe) hence the Material Universe is created for our enjoyment and we can lord over nature, so on many times we little gods fight one another because we are trying to lead each other, that is the diffculty. The moment you realise that you don't belong here and question about your existence, than you are known as a Human-being, if not we are no better than the animals just trying to enjoy our senses.
The Laws of Material nature(Goodness Passion and ignorance) are govern by 3 principle deities, Vishnu(goodness),Brahma(Passion) and Shiva(ignorance). The Law of Karma is another working energy which gives us a suitable body based on our own actions within this universe. The Goddess Durga(Kali) is the Material energy, she gives misery, destructions to all the living enities so that at least some would reform. These are all the agents of the lord who perform all these to serve him and yet the Lord himself controls everthing but remains aloof. We are born into enjoyment and suffering due to our own actions and has nothing to do with the Lord. The Lord remains aloof and yet controls everything indirectly, that is the power of the Almighty. He is too great.
Hare Krishna,
Based on the Bhagavad Gita and the Srimad Bhagavatam(Bhagavat Purana)(Vedic(Hindu) Scriptures)