In order to fully understand the trinitarian nature of God, let us look at the analogy of a human being to conclude our study on the subject.
We as humans have many different organs which are bestowed to carry out specific functions. For example, our hands are given to work, to embrace, to eat and so on, while our legs are given to transport us from one place to another. Our eyes are given to see while our ears to hear. Our mouth is given to speak, our tongue to taste, and our nose to smell. Our hands by themselves have no power to work and our legs by themselves have no power to walk or to run. Only when these organs are connected to us in whole can they function in their own domain. Our identity is formed when all of our organs are connected to us and it is only then they are able to function according to their design.
Just as a person can function perfectly when all of his organs are connected to him, so also God can function as God when the Father, Son, and the Holy Spirit are in perfect cohesion. They cannot be independent of each other.
God can reach out to any place, any time, in any form because God is omnipotent (all powerful), omniscient (all knowing), and omnipresent (present everywhere).
Science and God can definitely co-exist as long as science remains within the realm of discoveries and inventions. When science goes into the speculative realm and impose its speculation as real, this is where science and God cannot co-exist. The basis on which athiests call faith as speculative is itself speculative.