“Insouciant” can be remembered as “In + Soup + Ant”. Imagine an ant floating around in a bowl of soup with no care. It is just happy in a casual way. Nothing concerns it because it has food! Remember thus.
Imagine a mighty warrior secluding herself in her living quarters from others in her village before she goes out seeking quests. Thus, remember the word “Sequester” as a combination of Seclusion Quarters + Seek Quest. Remember thus.
The word “Quarantine” should remind you of “Quarter”, which is used to refer to rooms or lodgings, especially those allocated to people in military or domestic service. Imagine a large number of people who have been kept separate in quarters, which would mean that the people are in a quarantine. Remember thus.