1.Are feelings, emotions and facial expressions universal across borders, happy, sad, etc..?
I think these expressions universal.
happy---smile.
sad---cry, look at the ground
angry---frowning face
2. Try to name as many feelings as possible in Japanese.
うれしい delightful
たのしい joyful
くやしい frustrated
こわい afraid
なさけない miserable
しんどい hard feelings
しあわせ happy
ここちよい comfortable
めんどくさい bothered
たいへんだ oh, no!
どうしよう oh my god
おどろく suprised
あんしんする relief
うらやましい enviable
ざいあくかん guilty feeling
こうふん heat
なやむ worry
きんちょう nervous
まよう dither
3. Are there any feelings in Japanese that cannot be translated into English?
きょうしゅく
おかげさま
おそれいる
うちひしがれる(?)
I think there are more feelings in Japanese like above and vice versa.
In that case, we might have different mentalities.