The difference between 和谐，和睦 and 融洽？
和谐(adj): harmonious; balanced (between elements) | e.g. 氣氛和谐 (harmonious atmosphere); 和谐景象 (harmonious scene)
和谐(n): harmony | e.g. 達致和谐 (achieve harmony)
和谐(adv): harmoniously/ in harmony | e.g. 和谐共處 (harmoniously stay/live together; harmoniously co-exist)

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和睦(adj): friendly; harmonious (between people) | e.g. 關係和睦 (friendly relationship)
和睦(adv): harmoniously | e.g. 和睦共處 (harmoniously stay/live together); 待人和睦 (treat people with friendliness)

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融洽 (adj) harmonious (between people or element)| e.g. 關係融洽 (friendly relationship); 氣氛融洽 (harmonious atmosphere)
融洽 (adv): on friendly terms; on good relationship with | e.g. 相處融洽 (harmoniously interact/ live together)

Main difference is when they are in adjective role, 和谐 apply to elements, 和睦 apply to people and 融洽 apply to either people or elements
The difference between 和睦 and 融洽 is in the construction of the term. [和(peaceful/ in harmony) + 睦(befriend) = 和睦 (friendly/ harmonious) ]; [融(melt) + 洽 (arrange) = 融洽 (harmonious)