(1) You reconvene in the throne room, and Varel has made preparations to once again fill the Grey Warden ranks. You should have Anders, Mhairi, and Oghren in your party, and all three will partake in the darkspawn blood that either kills or transform one into a Grey Warden.
Oghren completes the rite without even losing consciousness. Anders passes out, but survives. Poor Mhairi, however, doesn't make it. There's nothing you can do about it; Mhairi dies in the Joining trying to realize her lifelong dream of serving the land as a Warden.
(2) After the Joining, you can leave at any time, but there are several things to do around the throne room first. You can speak with your NPCs, and if you click on the cask next to Oghren, you catch him drunk as a skunk guzzling from the tap. Listen to his amusing, drunken imaginations, but don't try to embarrass him with your dialogue choices or you'll end up with a disapproval rating.
Ambassador Cera sells runes and crafting gear, plus she'll enchant weapons and armor for you. On the other side of the room, Yuriah sells general goods. Comb the room for all the Warden-Commander possessions in the piles of books, armor stand, weapon stand, and personal storage chest (which serves as an extension of your party inventory, accessed only in the throne room).
The three main NPCs—Captain Garevel, Seneschal Veral, and Mistress Woolsey—hold the three main quests to progress through the game. Captain Garevel gives you the "Last of the Legion" quest. Veral sends you on the "Shadows of the Blackmarsh" quest. Mistress Woolsey entrusts you with "The Righteous Path" quest. Feel free to pick them all up now, or come back and pick up each one as you need it.