方便 1. noun--means "hand-washing" , "pee" , "shit" ; eg: 我去洗手间，方便一下 2. adv. --means "have time to do sth , conveniently ; eg: 我现在不方便接电话 , 等我方便的时候再给你打电话 3. adj. --means "convenient and make thing more easier " ; eg: 现在旅行很方便 , 坐飞机一下子就到了

便 has several different meanings. In the sentences you list, it is an adverb and means "就 or 即( just; simply; then; in that case:)". e.g.: then it is different; 那便不同 just do it like this; 这样做便可 If she doesn't appear this time, then she won't have any excuse. 如果她这次又不来， 她便没有什么藉口了。 Without a people's army the people have nothing. 没有一个人民的军队，便没有人民的一切。

有点像英语的 be going to , 表示一个动作马上发生。

here, 便 means 就. 我 便 先牽著爸爸出門。 = 我 就 先牽著爸爸出門。 就/便 highlights some fact. for example, - Tom, go to bed now! - 我不睡覺，我就不睡覺！我要看電視！ here, 就 highlights that "I dont want to sleep" but 就 and 便 have some difference in this example, u can replace 就 with 便. 就 is more powerful than 便 so when we talk, mostly we use 就. 便 is a lighter adv, it is used when we dont express much emotion. for example, 他說完，便走了。 We can say that we can use 就 to replace 便, but we cant use 便 to replace all the 就

1，可以当成“就，于是”讲，eg：我便下车了。 2，"方便" eg：这样最便捷了，这样便好了 3，便，音：[biàn，pián]。本义：[biàn] 就；方便，便利；[pián] 便宜；宽大的样子。