Those golden quests from clan are important. Without them, you won't have acess to higher ranking including a "2nd Role" or even 3rd when it will be avaible. It means no superiors skills to unlock and a clear disadvantage later on if you did not learn them whereas other players did.

Here a walktrough to the Road to Dragons quests but if you don't want any spoiler and prefer to discover the story, it is still possible to follow those guides. They only provide instructions if you are stuck.

There are some ways to complete them: Do them when you level up one by one or do them all at once right after getting you first clan role. You can of course do them whenever you want and those RTD quests cannot be gave up in the quest menu. Deciding to make them all once after the first role should be ok but it is not advised to do so when you are a vagabond and don't have any role yet since they will ask you to kill some low level monsters and if you are too high level, that won't be possible anymore to get any drops. Taking the drops in the ground if they are people grinding in that spot or trading with a low level characters those items quests are some possible solutions though.

To finish them faster you can use the following trick: save at the inn of a village you will realise the nex step and get killed by a guards for example in order to return to the clan base/inn faster. Recommanded if you are Bad Karma since you won't loose much of them and of course at 0% the next level in the experience bar.
You can also use Courriers Guild to travel faster between villages and will eventually have to lightfoot depending of the task.
Finally when you will have to complete 2 dungeons in a row, you should ask somone for help and get some HP pills or friends to deal more damage before the time run out and do not forget to break the pot behind the boss every time to complete the quest.

I you happen to encounter a bug and made sure that it is no more possible to complete the quest according to the guides then ask a GM to manually unlock your quest including Deimos - Cidopuck - Jester

Thanks to Fullneo and all the people who contributed in the guides above.