Learn German: Der Schulleiter soll krank sein. Stattdessen kommt die Vertretung. - The principal is said to be sick. Instead, the substitute is coming.

Because stattdessen is an adverbial connector. In German main clauses, the conjugated verb must always be in the second position (V2 rule). Since stattdessen occupies the first position in this sentence, the verb kommt has to take the second position, followed by the subject die Vertretung.

Could I use statt or anstatt here instead of stattdessen?

No, because they belong to different grammatical categories. Stattdessen is an adverb meaning 'instead', which perfectly starts a new standalone main clause. Statt and anstatt are prepositions meaning 'instead of' (which require a noun object immediately after them) or conjunctions (which introduce a subordinate clause).

Why is soll translated as 'is said to be' rather than 'should be'?

This is the subjective use of the modal verb sollen. When reporting hearsay, rumors, or unverified claims made by others, German uses sollen to mean 'is supposed to be' or 'is said to be'. Translating it as 'should be' here would wrongly imply that it is a good or desired thing that he is sick!

Is die Vertretung the standard word for a substitute person?

Yes. While it literally translates to the abstract concept of 'substitution' or 'representation', die Vertretung is the everyday term used in schools and workplaces for the actual person who is filling in for someone absent.