I think the best one for 'high in the sky' would be Taer = Lofty, high. Taer min eil = High in the sky, Taer min menel = High in the heavens. There's also Taur, which has the nuances of being 'mighty, vast, overwhelming' so to me that's more an edifice like Minas Tirith or a mountain.
Hall would indeed be as in a priest or other such figure, similarly Raud, but for people like Kings - 'noble, eminent, high etc.'.
Brand comes from a root that means 'height combined with strength/size/majesty'; you would use this adjective to describe someone like Elendil or Isildur, or something simultaneously tall and grand. Taer just means 'lofty, tall, high'.