Learn Italian: Iniziamo la seduta. Che il medium evochi lo spirito! - Let's begin the séance. Let the medium summon the spirit!

This is the exhortative subjunctive. Italian doesn't have a true third-person imperative form to say "let him do something" or "have him do something." Instead, you use Che + the present subjunctive. You can think of it as a shortened, implied command: "[I command] that the medium summon..." or "[I wish] that the medium summon..."

Why is there an 'h' in evochi when the infinitive is evocare?

To keep the hard "c" sound (like a "k") from the infinitive evocare. In the present subjunctive, regular -are verbs take -i endings for the singular forms. If we just wrote evoci, it would be pronounced with a soft "ch" sound. Adding the "h" maintains the original hard consonant sound.

Is medium treated as a normal Italian noun, and how would you say "the mediums"?

Like most foreign loanwords ending in a consonant, medium is treated as a masculine, invariable noun. This means it doesn't change its ending in the plural. To say "the mediums," you just change the article: i medium.

Isn't Iniziamo just the normal present tense "we begin"? Why is it translated as "Let's begin"?

In Italian, the first-person plural ("we") form of the imperative is completely identical to the present indicative. You tell them apart by the context or tone of voice. Here, it is functioning as an exhortation to the group: "Let's begin!"