1.Are feelings emotions and facial expressions universal across borders, happy, sad, etc..?
Hmm... Not all of them, I think. Also, there is big differences among individuals.
I got a good example! I think Japanese people feel embarrassing more often. They care about others around them too much. Do you think so?

2. Try to name as many feelings as possible in Japanese. ( 10 minimum) Now write the English translation.

１．うれしい（Happy, Glad）　　２．楽しい（Fun）　３．むかつく（Mad?）　４．寂しい（I miss something.）　５．わくわくする（Excited）　６．がっかりする、失望する（Disappointed, Depressed） 7. 悲しい（Sad）
８．怒る（Angry）　９．驚く（Surprised）　１０．テンパる（Freaked　out?）　１１．緊張する（Nervous）
12. 恥ずかしい（Emberrassing，Shy）

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

What about ’なつかしい’? My friend who is studying Japanese told me that it was hard to show the feeling in English. and...切ない？？？　I don't think up any English words to express this feeling. And, as Susan told us, ’渋い’and ’さすが’are Japanese emotions. ’渋い’was used to men and means intelligent, cool and calm. i also think it means he looks Japanese old-fashioned guy. Of course, it's good meaning. I like 渋い guys, lol.　　Then, さすが means that, I think, "I knew what you could do it." hmm...but, both are still hard to exactly express in english.