I am preparing for IELTS, but I can't hardly remember new words. I am preparing for IELTS, but I can hardly remember new words.

"can hardly/barely" is used to mean "hard time being able to". "can't" wouldn't be used here.

I am preparing for IELTS,; I can't hardly remember new words. I am preparing for IELTS; I can hardly remember new words.

At the same time, I can't hardly remember new Chinese words when I am reading. At the same time, I can hardly remember new Chinese words when I am reading.

At the same time, I can't hardly remember new Chinese words either when I am reading. At the same time, I can hardly remember new Chinese words either when I am reading.

There are so many characters that I've learned and promptly forgotten because I never use them ... 学习汉字的写法太难了。。。

It seems likeas if my brain has set up a wall to protect itself from the outside world since I graduated. It seems as if my brain has set up a wall to protect itself from the outside world since I graduated.

Nothing wrong with your choice, but this sounds a bit better.