Here's the basic rundown. To continue the storyline after completing the Sunjiang District mission, you have to go to either Cavalon (Luxon) or House zu Heltzer (Kurzick). At this point you take a corresponding "Befriending the Luxons/Kurzicks" quest. To complete the quest, you need to accumulate 10,000 unspent faction points with that Faction. When you have that amount, talk to the NPC for the quest and it will be complete. They will give you another quest to continue the storyline. It's Stolen Eggs for Luxon and Defending the Forest for Kurzicks. These quests will take you to either Gyala Hatchery for Luxons or Eternal Grove for Kurzicks. After completing this mission, you will do the Unwaking Waters mission, wherein you will be rejoined by the other side to complete the storyline.
Luxon and Kurzick faction points are account-based. You can do quests on any of your characters to accumulate the faction points you need and you can use the same 10k to complete the "Befriending" quest on all your characters.
The Luxon NPC's will not speak to you if you have more unspent Kurzick faction than Luxon, and vice versa.
Nothing I have outlined above is affected by whether or not you are in a guild, alliance, or to which side your alliance is aligned.
You can spend Luxon or Kurzick faction in 2 ways. First, you can trade it for Jadeite (Luxon) or Amber (Kurzick) which are rare crafting materials used for their respective armors. Or you can transfer faction to your guild, however, you can only transfer faction of the same Faction to which your guild is aligned. Transfer Luxon faction only when your guild is Luxon, and vice versa.
The titles relating to the Friend of / Ally of / Steward of / etc... are earned by donating faction to your guild in the amounts specified by each of the titles.
When you spend faction, either by converting it to crafting material, or transferring it to your guild, you lose an equal amount of the other side's faction points as well. So, if you a significant amount of unspent faction on one side, and you want to start earning faction on the other, if you don't spend the faction you already have beforehand, it will be wasted.
Also, you are limited to 10,000 unspent faction at a time, so if you are close to that amount, you may consider spending some to not waste the excess.
Hope this clears it up for you.