学校で毎年たくさんの科目がを勉強して、それから数ヶ月後に忘れた。

It should be 科目を rather than 科目が . Usually you should use を when what you are talking about is being acted upon, and が when what you are talking about is doing the acting. Because it is not the 科目 itself doing the acting, but rather you, it should be 　を.

私は一夜漬けが上手得意だから、科目の思い出とやり方は短期だ。

Use だから or なので when reasoning. Also, while 上手 works, it is more natural to say 得意 when you are talking about a skill you have. Therefore the beginning should say 私は一夜漬けが得意だから・なので
思い出 translates to memory, but usually implies sentimental and you wouldn't use it when you are talking about studying.

微積分が必要らしいけど、最後の微積分のクラスは1年以上前にから、ほとんどの技やり方を忘れた。

技 is a bit unnatural here, it's like saying you forgot the technique; it's more natural to just say you forgot how to do it (やり方を忘れた）

もう一度たくさんのことを勉強直し直すのは面倒だけど、私の悪い勉強方法が原因だから、あんまり文句を言わない方がいいと思う。

When you want to say "a lot of things", the phrase has の in it (i.e. たくさんのこと）
勉強直し is not a phrase - use the form "do" (as in you do studying, in Japanese する）before 直し, i.e. 勉強し直すのは面倒だけど
勉強方 should be 勉強法