Thank you very much for your corrections.
Here are some more sentences I'd like you to check.
1) An example of a desolate place is Frankenstein’s laboratory, where the scientist is confined in order to create the monster.
2) Frankenstein is not set in a dark castle like many Gothic novels. However, it presents some characteristics of them (Can you use “of them”?)
3) Grotesque elements are present in the description of the monster.
4) It is the old man's evil eye which vexes (also to vex) doctor Frankenstein.
He is confined in a small cottage (but “to live in a small cottage”?)
5) He takes him an hour to place (can you use “put”) his head in the room.
Another characteristic of the Gothic novel is the desolate environment: For example, the story begins and ends on the Arctic ice. (Can I use a period instead of a colon before For example?)
1) OK
2) Frankenstein is not set in a dark castle as many gothic novels are; however, it has some of those characteristics.
3) OK
4) It is the old man's evil eye which vexes Dr. Frankenstein.
He is confined to a small cottage.
He lives in a small cottage.
5) It takes him an hour to place/put his head in the room. This makes no sense to me.
Another characteristic of the gothic novel is the desolate environment: For example, the story begins and ends on the Arctic ice. (Can I use a period instead of a colon before For example?) <~~yes
1) Your sentence is grammatically correct. "An example of a desolate place is Frankenstein’s laboratory, where the scientist is confined in order to create the monster."
2) Yes, you can use "of them" in this sentence. "Frankenstein is not set in a dark castle like many Gothic novels. However, it presents some characteristics of them."
3) Your sentence is grammatically correct. "Grotesque elements are present in the description of the monster."
4) "Vex" can be used here, but "to vex" is more common and appropriate in this sentence. "It is the old man's evil eye which vexes (also to vex) Doctor Frankenstein. He is confined to a small cottage."
5) Both "place" and "put" can be used in this sentence. However, "put" is more commonly used in this context. "It takes him an hour to put his head in the room."
Regarding your last question, a colon is more appropriate in this context rather than a period. A colon is used to introduce an explanation, clarification, or example to what was mentioned before it. Therefore, using a colon before "For example" would help indicate that the desolate environment is an example of the previously mentioned characteristic of the Gothic novel.