Tricky
Briefly immortal
Let me clarify a little.Not at all true. They both try to answer exactly the same questions. There is no question religion brings up that science can not discover a reliable answer for. And, there is no question science can bring up, that religion could not possibly try to claim that it has some sort of answer for.
This statement contradicts your previous one, and only serves to demonstrate that they DO ask the same questions. All the freakin' time!
It does, when the claims are specific: They can be tested.
I will grant you that science would not have much to say for vague or untestable claims about god or gods. But, that does not mean science doesn't have any answers: The answer is that such an entity is superfluous. Its existence has no bearing on anything, and is therefore nothing to worry about.
The fundamental reason science and religion are incompatible, I think, is because of standards.
Religions' standards for obtaining knowledge are far, far, far weaker than those of science. So we find religious people coming up with ideas that sound good, but have not been verfied. As long as faith is part of religion, there won't be any way of getting around this.
Science accepts only the highest available attainable standards. The ideas it develops are usually non-intuitive, but are much more reliable to work with. There is no faith in science: Only challenge.
Many religions do address issues of science. In this, they are, in my opinion, straying outside of the regions that religion ought to address. But this does not mean that religion must address these questions. Religion can address questions of morality or of whether there is a life-after-death that lies outside the realm of the physical. As long as religion addresses questions that are specifically about the non-physical, it can happily co-exist with science, which is different from saying they are "compatible". As soon as religion strays into the region of the physical, then it leaves it's area of authority. It is quite unusual for a religion to be able to control itself like this, but some praticioners of Zen Buddhism and other purely philosophical religions manage to walk that narrow path.
I still think it is nothing but mental masturbation, but as long as they don't attempt to rewrite physics... well... masturbation is harmless.