就  means than you do something.

再 means than you decide whether you should do something, so the thing after 再 usually means something you haven't no do, undong thing.

where is different between 又 and 再 is 又 means done thing.

Please take a look at this page

Are these sentences correct grammatically ? If two kind of those sentences are correct, please tell me the difference between those two kind sentences which were use 再and 就？
1_你想想就买吧。 

你想买就买吧。

“就”represent ： the movement "想" has been finished already.

2_ 你想想再买吧。

“再”represent :the movement “想”  is not  finish yet, after the movement "想" finished, then sb. will make a dicision "买"or“不买”.

3_你的病还没有好，病好了以后就上课吧 。

你的病还没有好，病好了以后再上课吧。

“病” is not recovered yet,  so  “再” represent the thing “病” is not finish yet.
4_ 你的病还没有好，病好了以后就再上课吧 。

 “病好了” is a hypothesis,  “再”represent after the hypothesis “病好了” , you can go to class.

 “就” and "以后" represent the hypothesis that “病” has been already Cured.

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Why this sentence is incorrect according to grammatica?
到中国以后，这个电影我再看了一遍。再→又

“再” has the meaning of "又"which means again. “再” also has the meaning of “more” and “connecting link between two things”.

So  to avoid ambiguity and misperception，“又” is more appropriate than “再”.

The above is my opinion,  hope that I can be helpful.

Please take a look at this page

Are these sentences correct grammatically ? If two kind of those sentences are correct, please tell me the difference between those two kind sentences which were use 再and 就？
1_你想想就买吧。x 你想买就买吧   in this sentences 就=Conjunction   你想买，（那么）买吧

2_ 你想想再买吧。 再=then,先（first）想，想好了（Finished）（then然后=再）买  （你想想再买吧。=你想好了再决定到底买还是不买。）

3_你的病还没有好，病好了以后就来上课吧 。你的病还没有好，病好了以后，Conjunction，来上课吧 。
4_ 你的病还没有好，病好了以后再来（过来）上课吧 。病（Finished）再（Continue）上课 
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Why this sentence is incorrect according to grammatica?
到了中国以后，这个电影我又（又再次）看了一遍。

sorry,my English sucks