Wayward Son

Acquisition

Finish Long Way Home, then do the following:

Speak to Arianni in the Elven Alienage section of Lowtown - Day
Speak to Feynriel's father Vincento in the market in Lowtown - Day
Speak to the templar Thrask in the Gallows

Walkthrough

Feynriel is the son of an Dalish elf living in the Elven Alienage and a human merchant. He also has the talent for magic, something his Dalish mother hid out of fear of losing him to the circle until his nightmares could no longer be ignored as a warning signal.

Depending on who gave the quest, Hawke will either seek out Feynriel's father if the quest giver was his mother and then be directed to a retired templar named Samson or be sent directly to Samson if Thrask gave the quest. Samson is a retired templar, who resides in Lowtown and supposedly helps runaway apostates.

If Hawke gets the quest from Arianni then the dialogue options "I will stop him" followed by "Don't hold your breath" result in Bethany: rivalry (+10), Anders: rivalry (+5), and Aveline: rivalry (+5) (Questionable on that last one after patch 1.03).

Vincento will only tell Hawke where Feynriel is if Hawke is a mage or Bethany is in the party and you use the special dialogue option to prove yourself a friend to apostate runaways. An aggressive Hawke can also successfully threaten him to reveal Feynriel's location. Using the diplomatic option ("Make up for your neglect") will get Merrill: friendship (+10).

Talking to Thrask after getting the quest from Arianni can result in Aveline: friendship (+5), if you have her convince Thrask. Saying that you want to help Feynriel earns Fenris: rivalry (+10) and Merrill: friendship (+10), while saying that the boy is a menace and then choosing the diplomatic option to offer aid earns Fenris: friendship (+10), Anders: rivalry (+5), and Merrill: rivalry (+5).

NOTE: pc 1.03 does not give Anders: rivalry (+5) nor Merrill: rivalry (+5) when saying boy is menace and then choosing diplomatic option to offer aid, but does give Fenris: friendship (+10). Also verified in ps3.

EDIT choosing the boy is a menace option does gain 5+ rivarly with merrill on 360

Lowtown (Night)

Samson could not help Feynriel since the boy could not pay for his passage and instead sent him to someone who might give him free passage. Samson will tell Hawke to go check out the Docks.

NOTE: If you talk to Samson before being at this part of the quest, there will be a glitch and you will continue to see that you have to talk to him, but you can still find the location in the Docks.

Docks

Upon entering a private docking area, the party is ambushed by a group of slavers. After defeating them, Hawke walks in on a mage in mid transformation into an abomination. After dispatching the enemies, Hawke located a bill of sale directing the player to another group of slavers in Darktown.

The Abomination is actually Thrask's daughter and leaves evidence. Hawke can give this to Thrask with sympathy or blackmail him for two gold.

NOTE: Almost everybody disagrees with the blackmail; even Varric will give you rivalry. Isabela and Bethany will not be affected either way. Only Fenris will approve since Thrask is a Mage sympathizer and therefore hates the templar for not doing his job. If you blackmail you will get Fenris: friendship (+10), Aveline: rivalry (+10), Varric: rivalry (+5), Anders: rivalry (+5), Carver: rivalry (+5). If you keep his secret you will get Varric: friendship (+5), Aveline: friendship (+5), Anders: friendship (+5), Merril: friendship (+10), Fenris: rivalry (+10). Despite this, you can go to any site where you can gather your party members and choose to ONLY take Fenris before you talk to Thrask. This will give you +10 approval from Fenris, avoid any rivalry from other party members and Thrask will give you 2 Gold.

Darktown

If Fenris is in your party, Hawke can use him to make the slaver give him/her the information without a fight. Letting the slaver live results in Fenris: rivalry (+10), Carver: rivalry (+5), Aveline: rivalry (+5). Having Fenris make Danzig talk and then kill him results in Fenris: friendship (+10), Carver: friendship (+10) and Aveline: friendship (+5). No change to Isabela, Varric, Anders or Merrill. (I never got Fenris: rivalry (+10) after using the diplomatic option "I just want to talk" - 16.10.11)

It should be noted that there is actually no option to let Danzig live. Whether you choose the diplomatic or the aggressive conversation choice, Danzig will still insist on clapping you in irons which inevitably leads to a fight and his death.(pc)

After defeating them, the player will find a map on Danzig's body directing them to the Wounded Coast, into a slavers den.

WARNING: This part of the mission sometimes glitches. After killing the slaver, the map is NOT found in any of the dropped loot. This results in stopping game progression. The only way to fix it is to load a previous save or alter the quest using console commands

Slaver Caverns

After several tough battles including mages and Qunari, Hawke will walk in on the leader of the slavers who is holding a sword to the throat of Feynriel. Hawke can choose to bribe the slavers and pay for Feynriel's release. Alternatively, a Rogue Hawke can also choose to initiate a cut-scene in which he/she kills the leader with a throwing knife, thereby eliminating him from the following battle making things much easier. Also, if Varric is in your group, you can choose to have him speak to the leader and spin an amusing story to convince him to release Feynriel without a fight, gaining 3 in the process. You'll also get Varric: friendship (+5) if you chose this option. If Hawke chooses the violent option (I'll risk it) and attacks the slaver without any negotiation, Fenris approves for Fenris: friendship (+10) and Aveline will disapprove and you will receive Aveline: rivalry (+5). If you chose to negotiate with Fenris in your group you'll get Fenris: rivalry (+10) (negated if you tell Feynriel to go to Circle once he is released).

After the fight Hawke can opt to convince Feynriel to surrender to the Circle of Magi for his own good, or he/she can allow him to go live with the Dalish clan in the mountain.

If you allow Feynriel to go to the Dalish you can get Merrill: friendship (+10), Anders: friendship (+10), Aveline: rivalry (+5), Carver: rivalry (+10), and Fenris: rivalry (+10).

If you convince Feynriel to go to the Circle, You can receive Fenris: friendship (+10) (negated if you negotiated his release), Aveline: friendship (+5) and Carver: friendship (+10), Merrill: rivalry (+10), Bethany: rivalry (+10) and Anders: rivalry (+15).

If Anders is in your group you chose to let Feynriel go free you can get Anders: friendship (+10). If you tell Feynriel that there must be an alternative to joining the Circle and in the end tell him that he should do what he thinks is best you can get Isabela: friendship (+5). Hawke is then directed to go tell Feynriel's mother of his fate. Before you leave, go back to cave entrance and you will be attacked by a group of spiders for additional 110XP after you kill them.

Notes

Hidden Cave — There is a "hidden" cave atop the platform in the Slaver Caverns.

In the Slaver Caverns, after the dialog with Feynriel don't leave the cave through the near exit, instead go back through the cave to the entrance for a fight against some spiders, giving you some XP.
If you are seeking the Supplier achievement, be sure to grab the crafting resources in the Slaver Caverns. The Spindleweed is behind the mine cart near the entrance and the Deep Mushroom is in the back of the "hidden" cave up on the platform in the room where the first battle occurs.
Also, if not already obtained from earlier quests, there is some Glitterdust on a side road as soon as you arrive in the Wounded Coast.

Result

Feynriel will either go and live with the Circle or with the Dalish clan depending on Hawke's choice.

Allowing Varric to speak to the leader gains:

Varric: friendship (+5)

Attempting to talk down the leader or letting the leader go after letting Varric speak to the leader nets:

Fenris: rivalry (+10) (If you attempted to talk down the leader, Fenris will say, "Why are we talking?!", and a battle will immediately begin.)

Killing the slaver leader (Varian Ilithis) grants:

Fenris: friendship (+10)
Aveline: rivalry (+5)

Killing the slaver leader (Varian Ilithis) using the "special" dialogue option ("I don't need to step") available to a rogue Hawke results in no approval change.

Letting Varric speak to the leader, and still kill him afterwards grants:

Fenris: friendship (+10)
Varric: friendship (+5)

After the fight, you can choose to send Feynriel to the Mages Circle, or letting him live with the Dalish.

Convincing him to go to the Circle has companion effects:

Aveline: friendship (+5)
Merrill: rivalry (+10)
Fenris: friendship (+10)
Anders: rivalry (+15)
Carver: friendship (+10)
Bethany: rivalry (+10)

No impact on Isabela

Sending him to the Dalish has companion effects:

Anders: friendship (+10)
Bethany: friendship (+10)
Aveline: rivalry (+5)
Merrill: friendship (+10)
Fenris: rivalry (+10)
Carver: rivalry (+10)
Isabela: friendship (+5) (only with the "you deserve to choose for yourself" option; on PC it is "Do what you think is right.")

Rewards

Runed Silverite Ring and some coin, regardless of how the quest is handled. If the Circle option was chosen, then: Anders: rivalry (+5) upon receiving reward.

If you tell Feynriel to go to the Dalish camp, he will be at Sundermount for the remainder of Act 1. Travel there for a brief dialog with him and Keeper Marethari, after which the Keeper will give you 1 for bringing him to them. This decision also triggers an encounter at Sundermount (with no journal entry) at the start of Act 2. This will trigger the quest Night Terrors in Act 2.

If you tell Feynriel to go to the Circle, he will be at the Gallows Courtyard later in Act 1. Additionally, the quest Elves at Large will be available from the Chanter's Board in Act 2. Night Terrors will not appear, if you choose this option.

Crafting Nodes

Inside the Slaver caves you'll find a Spindleweed node and a Deep Mushroom.

Trivia

Upon finding the map to the slaver den in the chest in Darktown, a sarcastic/witty Hawke may make a joke about the Wounded Coast, saying it must be near the "Injured Cliffs", the "Limping Hills", and "Massive Head-Trauma Bay".