Separable verbs are only separated in sentences with a Satzklammer. That are basically main clauses with the verb in the second position:
Du willst dort hin.
Subclauses do not have a Satzklammer. The verb comes at the end by default and is never seperated:
Dort, wo du hinwillst.
Possible and stylistically maybe better, however, would be to use the ...
The capitalized Du is old orthography. Before the Rechtschreibreform in the 1990s is was common in letters to write forms of du (du, dich, dir, dein etc.) with a capital D to honor the recipient.
"Hinwollen" is a composed verb here. See https://www.duden.de/rechtschreibung/hinwollen
In a subordinate clause like this, there's no reason to separate ...
Mit is not a preposition, but an adverb here. See the Duden page for a detailed listing of several use cases.
I will answer your questions separately:
What role does mit play here?
I think the most important function of mit is to express togetherness:
Als Max einen Fallschirmsprung plant, meldet er Ernst gleich mit sich zusammen an.
However, you can think ...
You are right, this sentence is wrong. I don't think this is a regionalism or sociolect. I guess it is just an editing mistake - most probably another verb was used before and the superfluous zu was not removed after editing.
Correct would be:
Dann brauchst du noch einen Kohleklumpen, um das Feuer anzufachen.