Since science is not a thing, No.

Since science is a method used to determine reality, Yes.

Every new insight of science opens up a hundred mysteries. We are abjectly ignorant of the nature of Ultimate Reality, and will remain so.

There are boundaries to what science is capable of doing. It can only answer questions that can be answered by empirical data. The statements in question have to be falsifiable, in other words there would have to be facts that could be found which make those statements false. For instance the statement that there is an invisible god is not falsifiable because there is no empirical data which could falsify the claim.
Also science can't tell us what we should do or should like, what is good or how society should function. It can inform those areas because in order for us to decide what we should do we have to know what is possible for us to do. In order for us to decide what is good we have to know things we can categorize into good, bad, tasty, sexy ect.
Also math and logic are tools that science can use but the truthfulness of their statements are independent of empirical data. So something having a rational explanation and it falling into the domain of science is not a necessity.

There are serious challenges to science explaining everything. One that currently seems impossible is to know anything about conditions before the Big Bang. Similarly, the visible universe is a little less than 14B light years distant, and part of the Universe is beyond that distance; however, space-time is receding at the speed of light at that distance, and it is impossible to see beyond. We cannot see inside a black hole, and the smallest things, whatever they are, cannot be seen with any tools we can imagine. Thus, it seems unlikely everything will ever be known.

No

As mentioned, explaining consciousness itself is probably the biggest challenge. Keep in mind too that philosophy, or lack thereof, comes before science. Philosophy sets the stage for science. Kant's philosophy, for example, has had a big impact on the interpretations of quantum theory for many scientists.

Spock says so.....

I think the real challenge for science is to explain qualia. That is to explain the mechanism of our experiences and thoughts. To explain consciousness itself, and how and why it arises.