I believe " أخذ راحة" means " He took a rest" while " أخذ راحته" which sound more colloquial means " to feel at home/ to feel free/ to feel comfortable and relaxed". I also believe "أخذه راحة" conveys no meaning. If you want to say" He was disturbed" قلقت راحته" ( colloquial) or " اختل وقت راحته"( sounds very formal)... Hope you find the answer helpful :)

He chills (إنه يرتاح ) and His chill was disturbed. (إختل أو إضطرب وقت راحته)

أخذ راحته في العمل (في العمل) 1 أخذ راحته بعد العمل، أو: أخذ راحة بعد العمل (بعد العمل) 2 different meaning, 1 means: "getting too comfortable at work", while 2 means:"a time for rest after work". the meaning is always related to في، من والله أعلم

This one is super funny, useful, and easy exception to use. خذ راحتك which means "Make yourself home". ( when you have a friend coming over, and after kisses and hugs - Arabic way of welcoming- you take them to your room and say " خد راحتك " they can take their shoes, ley casually in the couch, play with your PS4, or go through books in the library. ) أخذ راحته Which means that someone was so relaxed and they take their time, without worrying about anything- and may be too much - May be you went to a restaurant and the chief there he takes so much time to do one dish and he is really taking his time, you can really say واخد راحته even you are very hungry. And one more example, a student 2 weeks from the finales exams, and he spent 2 days on the introduction chapter, for instance, he is really واخد راحته على الأخير and probably he will be in big trouble soon. this is the idiom meaning of those phrases, I hope you got the meaning, please write back if you need more explanation, or if you grasp the meaning please say so. Keeep learning and good luck