Why not 请帮助我？
I learn Chinese for two years and this is the first time i saw 帮 separate, without 助
很 is very. 很忙 very busy
Just 忙 is busy
Here the 很 is needed for grammatical reasons. In the phrase structure "noun is adjective"(e.g. "the cat is busy", you need to use 很 as "is". In other contexts, like "noun is noun" ("the cat is a mother"), you translate is with 是。
No, 很忙 can also be just "busy". This "Chinese exaggeration" is like SUPER common. ;-)
很 is used like a particle, 我忙 is incorrect, you need a particle beetwen then.