Correct usage/ that/they as complete sentences
These are called sentence fragments. It is common practice to use a dependent clause as a separate sentence when it follows clearly from the preceding main clause in journalistic writing; it is often used for emphasis and style.
Examples in Journalese writing:
The current city policy on housing is incomplete as it stands. Which is why we believe the proposed amendments should be passed.
Some may disregard you for using such practices in formal or academic situations, personally, I believe it is completely fine to start a sentence with a conjunction:
But it’s these conflicts between life and death that are the works' main themes. They echo an important principle in that we shouldn’t fear or challenge death, or the nature of death. That we can meet it half-way by valuing life and respecting and not harming others.
The sentence beginning with 'they' is a complete sentence, its antecedent is "these conflicts". So they can be replaced with these conflicts: These conflicts echo an important principle...
However, the that-clause can be seen as a dependent clause preceding from the main clause, "They echo an in important principle...":
They echo an important principle; in that we shouldn't fear or challenge death, or the nature of death ; that we meet it half-way be valuing life and respecting and not harming others.
and so it should not be separated. Usually, a dependent clause can be the head of a sentence if it does not precede as a main clause from the previous sentence. However, as you can see if it were not separated it would be an extremely complex sentence. Personally, I would reword it as:
They {these conflicts} echo an important principle: that we shouldn't fear or challenge death, or the nature of death and that we meet it half-way by valuing life and respecting and not harming others.
Still, I'd prefer:
They echo an important principle in that we shouldn’t fear or challenge death, or the nature of death. That we can meet it half-way by valuing life and respecting and not harming others.
As it is much easier to understand and the emphasis is clear. In terms of rhetoric, the that-clause is syntactically parallel to the but-clause:
But it's these conflicts between life and death that are the works' main themes. // That we can meet it half-way by meet it half-way by valuing life and respecting and not harming others.
How?
[Conflicts in life are tiresome], but it's these conflicts between life and death that are the works' main themes.
They echo an important principle; in that we shouldn’t fear or challenge death; ... that we can meet it half-way by valuing life and meet it half-way by valuing life and respecting and not harming others.
The things in [] in (1) is just my interpretation of what could precede the but-clause.