House Guildmage's first ability doesn't tap the creature. It can target any creature, tapped or untapped. If that creature is already untapped at the beginning of its controller's next untap step, the effect won't do anything.

You perform the actions stated on a card in sequence. For some spells and abilities, you'll surveil last. For others, you'll surveil and then perform other actions.

When you surveil, you may put all the cards you look at back on top of your library, you may put all of those cards into your graveyard, or you may put some of those cards on top and the rest of them into your graveyard.