You've said two things that accurately define science, sort of:
tesla writes:
does what we see, what we smell, what we touch, what we hear, what we taste, exist in an idea?
What you said up until the "exist in an idea" portion makes good sense. Science studies the natural world, the world available to our senses. Science takes for granted that the world of our senses exists. Questions about the reality of existence are philosophical, not scientific.
in conclusion: existence can be studied by science.
When you use the word "existence" it makes your meaning ambiguous. Do you mean the world of our senses, which would be science? Or do you mean the existence of philosophy, such as existentialism and so forth?
ideas are tentative. (may be...could be)
things are facts to be studied.
Keeping things simple, hypotheses are very tentative, theories are tentative, facts that we gather through observation and experiment are certain. It's actually not this simple, but I hesitate to introduce nuances until this point becomes clear.
So science can study anything we can observe, even if we can only observe it indirectly. We can only measure temperature indirectly, using a thermometer. We can only see cells indirectly, using a microscope. We can only detect electrons indirectly via special instruments.
But science cannot study things we can't observe. To study God science requires that he be in some way observable. Science will never assume the existence of anything for which there is no evidence. And defining God as a synonym for all of reality is just playing word games, plus most Christians wouldn't agree with you anything, since they believe that God transcends reality.
--Percy