1.Are feelings emotions and facial expressions universal across borders, happy, sad, etc...?
Yes. I think feelings emotions and facial expressions are very similar all over the world. For example, we open our eyes wide when we are very surprised, we smile when we are happy and we raise our eyebrows when we are irritated or angry.

2. Try to name as many feelings as possible in Japanese. ( 10 minimum) Now write the English translation.
English & Japanese
　①happy : 嬉しい
　②sad : 悲しい
　③angry : 怒る
　④painful : 苦しい
　⑤fun : 楽しい
　⑥nostalgic : 懐かしい
　⑦scary : 怖い
　⑧exciting : わくわくする
　⑨disappointed : がっかりする
　⑩lonely : 寂しい

3. Are there any feelings in Japanese that cannot be translated into English?
Yes. For example, "setsunai(せつない)", "yabai(やばい)","bimyou(ビミョー)"