Sherlock Holmes is my favorite book and its drama is awesome.

I try to watch without Japanese subscripttitles, however it is difficult for me because the casts speaks so fast.

I try to watch without Japanese subscripttitles, however it is difficult for me because the casts speaks so fast.

I keep on trying to hearlisten and catch the sentences.

"Hear" is similar to 聞こえる. "Listen" is similar to "聴く"

"To hear" is something you do passively.
"To listen" is something you do actively.

For example:
"I hear the people talking." means the people are talking and their voices are audible.
"I listen to the people talking." means, you are intentionally paying attention and trying to understand their conversation.

I try to watch without Japanese subscripttitles, however it is difficult for me because the casts speaks so fast.

Often we use the term subtitles in the US
The cast already refers to a group of people, so it would only be plural (casts) if you referring to multiple sets of casts
Speaks is plural since multiple people (the cast) are speaking