Learn Swedish: Varde ljus, och Gud vare tack. - Let there be light, and thanks be to God.

Varde is the optative form of the archaic verb varda, which means 'to become' (similar to bli). You will almost exclusively see it in this specific biblical quote, Varde ljus ('Let there be light'). In everyday modern Swedish, you would just use bli instead.

Why does the sentence use vare instead of är in Gud vare tack?

Vare is the optative mood (present subjunctive) of vara. Instead of stating a fact like är ('is'), the optative expresses a wish, hope, or exclamation. Here, it translates to 'be' in the sense of 'may there be', making the phrase mean 'Thanks be to God.'

How do you build this optative form, and should I start using it in my own sentences?

You form it by adding an -e to the verb's stem. The stem of vara is var-, creating vare, and the stem of varda is vard-, creating varde. However, you should not try to build new sentences with this! The optative mood is basically dead in modern Swedish and is strictly limited to recognizing fixed, historic expressions like these.

In Gud vare tack, why is Gud at the start of the clause if 'thanks' is the thing being given?