After his father's death, Gilbert has to take care of his family, as his mother is unable to do so asbecause she is deep inly depressioned and overweight.

"as" can also be changed to "since"

Gilbert's internal struggle is the fact that he can't have his own life, and also the acceptance ofs well as accept his mother.

He has to take care of his family, but he doesn't take care of himself, t. There's no joy in his life.

You could say "...as there's no joy in his life", but making it it's own sentence gives it more weight.

She also acts as emotional support and helps him understand himself, t. Thanks to this, he slowly starts to accept and comprehend his mother.

He regains joy, and his life is not so static anymore.

After his father's death, Gilbert has to take care of his family, with his mother is unable to do so as she is deep in depression and overweight.

I altered the sentence a little so that it flows better.

Gilbert's internal struggle is the fact that he can't have his own life, and also the acceptance ofnor learn to accept his mother.

I rewrote the second half of the sentence based on what you wrote in the second-last sentence ("he slowly starts to accept ... his mother"). But it is also possible that you meant: "Gilbert's internal struggle is the fact that he can't have his own life, nor gain the acceptance of his mother."

He has to take care of his family, but he doesn't take care of himself, and there's no joy in his life.

Adding the "and" might help the sentence flow better.

When he meets Becky, he learns to live life again and discovers new ways to live,; she brings him happiness.

She also acts as emotional support and helps him understand himself, and thanks to this, he slowly starts to accept and comprehend his mother.

He regains joy, his life is notno longer so static anymore.

I rephrased the sentence so that it sounds more fluent.