How are 立ち向かう & 直面する different? They both seem to mean "to face"?

Question:

Also define, 抱える、持つ、つかむ、and くわえる because they all seem to mean to hold?

Please define each. Arigatou Gozaimasu!

Answer:

Basic rule is, it's all about context and nuances.

That said:
立ち向かう implies a more positive attitude than 直面する.

立ち向かう = to face
直面する = be faced with.

抱える = to hold in one's arms or under one's arm　
持つ = a neutral word for "to hold" or "to have"
つかむ = to grab, to grasp
くわえる = to hold in one's mouth/between one's teeth

起こる sounds more formal/academic than 生じる (like "happen" versus "occur".)

You seem to be in need of a good Japanese to English dictionary.
I use this and highly recommend it.
http://www.amazon.co.jp/gp/switch-langua…

*Edit*
- 起こる sounds more formal/academic than 生じる (like "happen" versus "occur".)

Oops, I mean 生じる sounds more formal/academic, like "occur" as opposed to "happen". Also, certain things, such as earthquake, can only 起こる, never 生じる, which also means "to be generated".