Seems when discussing or arguing any field of science, there is always a limit on how far the conversation can proceed without reaching the limit of that said field or being passed over to some other field of science.
Indeed. When discussing the fundamental properties of biochemical molecules, you invariably cross over from chemistry into physics.
Science is very compartmentalized. For instance Evolution, A Evolutionist will say well we can tell you how things evolve but not tell you from what everything evolved from and at what point did non life become life and how did that happen.
Not entirely. The theory of common descent posits the existence of a single organism that lived about 3.5 billion years ago, from which all modern life is ultimately descended (hence, 'universal common ancestor'). The evidence for evolution is primarily concerned with a) demonstrating common ancestry, and b) the proposed mechanics of evolution.
So, the evidence for evolution supports the existence of this common ancestor, even though the theory itself doesn't explain
where it came from, or how it got there.
But, that doesn't mean there isn't
another theory that tells us these things. Objecting to evolution because it doesn't explain the origin of that initial organism is moot, as we have another theory to tell us that very thing - abiogenesis.
I like to think of it as an overarching narrative. We start with the interstellar dust cloud that condensed to for the Sun, then the Planets, then the Moon formed, then the Earth cooled, then the oceans formed, then simple organic molecules formed, then life formed, then a plethora of taxa evolved, then humans evolved, then civilisation emerged, then the Internet was invented, and then I was able to talk to you.
This long chain of events isn't invalidated just because there are multiple theories from multiple fields contributing to it (cosmogony, geology, chemistry, biology (evolution, abiogenesis), sociology). Theories tend to 'hand off' to one another.
Big Bang same thing, science can explain the expansion but not the origin of the "little ball of energy" or what it exploded into.
Correct. The evidence is enough for us to be sufficiently certain the singularity existed, but there is, as yet, little evidence or theory to tell us where that singularity came from.
This trend continues into every subject and field. So my question is, is there a field of science that works on connecting all the dots and filling in the blanks from one theory to the next?
A new theory which connects two dots generally makes reference to hitherto established knowledge - abiogenesis, for instance, makes reference to the established conditions of prebiotic Earth and the conditions of post-biotic Earth. There isn't one single field that works on connecting the dots, but rather, gaps in scientific knowledge are worked on by scientists from every field - psychologists work on closing gaps in our knowledge of the mind, etc.