"τα" sounds like "α"
No, the τ is there, but it's pronounced at the end of καλεί, as it should be. Because of that, it is weak, but it sounds perfectly right and natural.
The wizard invites ghosts??
Invite is προσκαλώ.
Is καλεί etymologically related to "call" ? Seems pretty obvious
Looking at etymological dictionaries, it seems that the similarity is coincidental.
What about orders the ghosts?
"καλώ" means "call, invite" for "order" you would use "διατάζω" (unless you meant "order" as in a restaurant then use "παραγγέλλω")