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1.Are feelings emotions and facial expressions universal across borders, happy, sad, etc..?
Yes,. I think so,but American and European, they express thier emotion much more with thier whole body than Japanese.

2. Try to name as many feelings as possible in Japanese. ( 10 minimum) Now write the English translation.
☆暑い⇒hot
☆寒い⇒cold
☆眠い⇒sleepy
☆いらいらする⇒irritate
☆しんどい⇒feel bad
☆腹立つ⇒angry
☆悲しい⇒sad
☆うれしい⇒happy
☆疲れた⇒tired
☆暇⇒bored
☆楽しい⇒enjoy
☆恥ずかしい⇒ashamed
☆緊張する⇒nervous
☆寂しい⇒miss
☆にくい⇒hate
☆惨めだ⇒miselable
☆こわい⇒scared

3. Are there any feelings in Japanese that cannot be translated into English?

きもい、うざい、うっとおしい(●′Å`◎)-vV☆