After a quest, I am usually presented with the option of clicking on the drama-happy-sad-face icon (see image) which unveils new quirks, sometimes good and sometimes bad. Do I have to click on those? I mean if I don't click on it and just continue to the hamlet, do the new quirks just stay hidden and inactive?
You do not get to choose which perks or quirks your heroes gain, and you don't get to choose not to reveal them. The lands around the Darkest Dungeon are cruel and unrelenting.
You can however, at some expense, have your heroes treated at the Sanitarium and to have a quirk removed through brutally efficient aversion therapy.
((Note: once a quirk becomes "locked in" as seen by the red skull in a red square in front of it, it becomes significantly more expensive to remove. With gold as scarce as it is, think carefully as to whether you feel the expense is worth your adventurers' sanity.))