Kivan actually has two minor quests, apart from the fact that his interest ("Big Quest") is more than any other NPC tied up with yours. His Primary Quest is really hunting Tazok, at least until the conclusion of BG Tutu. BG1 NPC ties this Quest in with yours at all levels, with direct interjections, responses, and expansion of the original content. For Kivan's extended story arc, see Domi's BG2 Kivan Mod, part of the Lands of Intrigue Project, and available separately at the present time.
Two subquests for Kivan are available: one Bounty Hunter attempting to collect, and one Sea Elf who has some difficulties.
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Kivan Quest 1
A bounty Hunter shows up on the City side of the Baldur's Gate Bridge ( http://www.forgottenwars.com/bg1/ar0900.htm ) area FW0900, waiting by the side of the road with her wolves. She will involve the party in a quick conversation and if Kivan is in the party, there are choices of either killing him or the Bounty Hunter. You can interact and even combat Imanel Silversword separately from Kivan, but the primary content is driven by having Kivan in the party.
Kivan Quest 2
If you visit Area FW3100 ( http://www.forgottenwars.com/bg1/ar3100.htm ), coordinates [3417.974] at night, you will run into a Sea Elf with a quest for Kivan.
If you choose to not help Jozzi, then
you eventually get raided, a battle with sea creatures, and all is resolved.
/* Scene 3 (if did not help Jozzi, she shows up with 5 other Sahuagin) */
IF ~Global("X#KivanSea","GLOBAL",8)~ SEAL3.1
SAY ~Here be more drylanders ready for eating. Let us feast!~
= ~Regretting our meeting, did I not tell you that you be, drylander?~
IF ~~ THEN DO ~SetGlobal("SeasnakeAttack","GLOBAL",2)
If you choose to help Jozzi, you get the largest
amount of content, a battle, and choices.
Action is carried forward in cutscenes, so there is not much troubleshooting you can do here unless you know coding.