英文语法：be动词和助动词有什么区别?

英文语法：be动词和助动词有什么区别?
一个虚拟语气句子：
If there was no gravity, we should not be able to walk,该句是错的,应该写成:
If there were no gravity, we should not be able to walk.
还有同种情况的句子：If I were rich, I should help the poor.
If my theacher were here, he might be able to help.
但是问题来了,下面这个句子：
If it weren't raining, I would not stay in the classroom.又是错的,应该写成：
If it wasn't raining, I would not stay in the classroom.解释是：此句中be为助动词,而非be动词.
希望高手帮我解答一下这个句子,另外说一下be动词和助动词如何区分,谢谢
最后一句还真是助动词，刚才突然想明白一点了。请高手给说说怎么能比较简单地判断出来be动词还是助动词，目前这两个答复我实在不能采纳为答案。