You must have 'Sebastian' from the Exiled Prince DLC in your party when talking to certain people in certain quests. There are ample opportunities to gain maximum Friendship or Rivalry throughout the campaign. Personally I found Friendship easier and more beneficial but I have listed all instances for both sides below.
.........FRIENDSHIP....................................................................................................If you are following the Walkthrough and have come short of max Friendship, you'll most likely be doing the 'Mirror Image' quest for Merrill now. Make sure you have Sebastian in your party, and near the end of the quest, save just before you talk to 'Keeper Marethari', then in the conversation choose 'The Keeper is right' and then 'No, I can't do that'. This should max your Friendship now. Then reload the save and continue to follow the Walkthrough by selecting 'The Keeper is right', but then 'Fine take it'.
Below are all instances of gaining Friendship with Sebastian, with the exact amount of Friendship points in brackets and 'F' indicating Friendship:
Act 2A Bitter Pill: When the slaver demands Fenris be turned over, respond "He is not a slave!" (5F).
Dissent: Hawke refuses to help Anders (15F).
Dissent: Hawke stops Anders from harming Ella (15F). An additional (5F) if Hawke then says, "Just what it looked like." Upon meeting Ella outside the tunnels, and (5F) if Hawke then tells her to return to the Circle.
Family Matter: Hawke allows Bartrand to live (10F).
Fool's Gold: Accept the job (5F).
Fool's Gold: Tell Emrys that he/she will save Merin (10F).
Fool's Gold: Save Iwan and the truth comes out about Merin's death (5F).
Night Terrors: Tell Marethari "I understand" (that Feynriel must not become an abomination) (10F).
Note: To avoid getting this point negated by 10 Rivalry, start the quest without Sebastian. Postpone the quest when Arianni asks if you are ready. Then, go to Merrill's house, put Sebastian in your party and resume the quest.
Offered and Lost: Warn Elthina ("Someone used your seal") (10F).
Note that the option "You're useless" in the same conversation will yield rivalry points, if it wasn't chosen earlier in this Act.
Offered and Lost: Say "Varnell and the others die" (10F).
Offered and Lost: Tell the Viscount not to hide what happened (10F).
Prime Suspect: If Hawke begins the conversation with Emeric along a diplomatic and then a humorous line of conversation until Sebastian comments that "this is a worthy cause" and then finishes with the diplomatic option to accept the quest.
Note that if Aveline is in the party, her responses will override this and the approval gain will not be possible (5F).
Questioning Beliefs: Tell Sebastian to remain a brother in the Chantry (15F).
Repentance: When speaking to Allure, if Hawke says, "That's a good point" (15F).
Repentance: When speaking to Flora at the end of the quest, choosing, "You were all victims" (5F).
Repentance: Choosing the following options upon returning to the Chantry: "That's a good question", "What do you want to do?", and "Listen to your heart" (10F).
The Starkhaven Longbow: Give Sebastian the gift with the Diplomatic dialogue option (10F).
The Starkhaven Longbow: Give Sebastian the gift with the Witty dialogue option (5F).
Act 3Alone: Convince Fenris to allow Varania to live (5F).
Justice (quest): You can earn up to (30F). Refuse to distract the Grand Cleric after helping Anders to gather ingredients (15F). Go to the Chantry and warn Elthina via a special dialogue option. This must be done before accepting the Faith quest (15F).
Faith (quest): Making the following choices during the quest can yield up to (55F). When asked to meet with Sister Nightingale, reply "Of course" (10F). Then choose "We'll go right now" (15F). Tell Sister Nightingale that the situation in Kirkwall is not as bad as it seems (15F). In the final conversation when Grand Cleric Elthina refuses to leave, reply "Please Reconsider" (15F).
Haunted: After the battle, give the idol piece to Sandal to craft a rune (10F).
Finding Nathaniel: In the Deep Roads, when you talk to Nathaniel Howe, Sebastian will express approval of 'rescuing a warden in peril' (10F).
On the Loose: When you talk to Meredith, if you're willing to help the templars (5F).
On the Loose: During the final conversation with Walter and Cricket, reply diplomatically or aggressively (5F).
Legacy DLCAltar of Dumat: Defile the Altar (5F).
Legacy: Side with Janeka (5F).
..........RIVALRY........................................................................................................Below are all instances of gaining Rivalry with Sebastian, with the exact amount of Rivalry points in brackets and 'R' indicating Rivalry:
Act 2
A Bitter Pill: During the first ambush, offer to make a deal (10R).
Blackpowder Courtesy: Kill the dwarf Javaris Tintop (15R).
Dissent: There is a cap of (15R) that can be earned when accepting the quest. Let Anders kill Ella (10R) or save her, choose either non-aggressive answer and tell Ella to go somewhere safe (5R).
Family Matter: Have Varric kill Bartrand (10R).
Fool's Gold: Tell Emrys that you'd rather have the weapon than save his brother (10R).
Grand Cleric Elthina: Choosing "You're useless" when speaking to her will net (5R).
Note that you will gain his friendship if during Offered and Lost you will also choose "Someone used your seal."
Mirror Image: Give Merrill the Arulin'holm (5R).
Night Terrors: Choosing the diplomatic dialogue when talking to Arianni, followed by accepting the quest (10R).
Note: Approval will only count if a small cutscene of Sebastian disapproving of the quest is shown.
Night Terrors: Tell Marethari that you will not kill Feynriel (10R).
Offered and Lost: Tell Ser Varnell to kill the Qunari (5R) When the Viscount asks what should be done with the bodies, tell them to burn them (10R). This will lead to (15R) total.
Prime Suspect: Picking the third aggressive response when talking to Emeric (5R).
Questioning Beliefs: When speaking to Sebastian, the first and second set of choices all take you the same place. In the third set, choose Starkhaven (15R).
Repentance: When speaking to Allure, choose "Don't listen to her" (15R).
Repentance: When speaking to Flora, choose "Don't try to wiggle out of this" (5R).
Repentance: During the final conversation back in the Chantry, choose "You must take back your land" (10R).
The Starkhaven Longbow: Give him the gift with the Aggressive dialogue option (10R).
Act 3Alone: Hand Fenris over to Danarius (10R).
Alone: Let Fenris kill Varania (5R).
A Murder of Crows: At the end of the quest, sleep with the assassin when given the opportunity (5R).
Faith: In the conversation with Sister Nightingale, tell her it's time for a holy war (15R).
Faith: In the final conversation when Grand Cleric Elthina refuses to leave, reply "Fine, your choice" (15R).
Haunted: Let Varric keep the shard of the idol (10R).
A New Path: In the beginning of the quest, if you force Merrill to talk to Marethari without asking by just talking to Marethari beforehand, and you pick the option to ask Marethari to help fix the Eluvian (5R).
No Rest for the Wicked: When approaching the room with Isabela at The Blooming Rose, respond with the aggressive answer (5R).
No Rest for the Wicked: During the final conversation with Castillon, allow Isabela to trade the incriminating documents for Castillon's ship (5R).
On the Loose: When talking to Knight-Commander Meredith, tell her "I am no ally of yours" (5R).
On the Loose: During the initial conversation with Walter and Cricket, reply sarcastically or aggressively (5R).
On the Loose: During the final conversation with Walter and Cricket, reply sarcastically (5R).
On the Loose: During the final conversation with Walter and Cricket, refuse to give them money (5R).
On the Loose: Allow Emile de Launcet to go free (5R).
Legacy DLCAltar of Dumat: Offer a tribute to Dumat (5R).
Legacy: Side with Larius (5R).
Special thank you to http://dragonage.wikia.com/
