Important tip: You can ONLY reach the three/four trials area from the quest screen, and the 'proceed' button disappears after you have done one of each. You can complete each twice per day (with a 10min cooldown) but if you back out of that screen you wont be able to go back, so you need to make sure to stay in the trials menu while waiting the full 10mins to get all of them.
Also, you are not oblivious for not knowing about the trials quests; they were a temporary thing added for an event only like 2months ago, which the devs only partially removed from the game afterward (for a little while there was a clearer way of accessing them from the quest menu, which they deleted after the event ended)