It's another cloudy day, the kind of winter weather that I hate the most. It's another cloudy day, kind of winter weather that I hate the most.

It's another cloudy day, the kind of winter weatherday that I hate the most. It's another cloudy day, kind of winter day that I hate the most.

I hate the most.

I hate the most.

The gray sky always makes me feel unenthusiastic. The gray sky always makes me feel unenthusiastic.

This is a simple conjugation error, your sentence is correct otherwise! Examples: The gray sky brings rain where I live.

The gray sky always make me feel unenthusiastic. (Lethargic, dispirited, sad) The gray sky always make me feel unenthusiastic. (Lethargic, dispirited, sad)

The gray sky always makes me feel unenthusiastic. The gray sky always makes me feel unenthusiastic.

Thankfully it's the weekend. Thankfully it's the weekend.

Native speakers tend to use 'the' before some ideas, especially 'the weekend'. Examples: Today was a good day. The weekend will be even better!

Thankfully it's the weekend. Thankfully it's the weekend.

This is a moment when I am thankfully it's weekend. This is a moment when I am thankfull it's weekend.

I'm planning to start with "Welcome to Derry". I'm planning to start with "Welcome to Derry".

This sentence is correct. In writing, we tend to surround the titles of books and movies with quotation marks ("").

I really like the way it builds a horrorn atmosphere of horror. I really like the way it builds an atmosphere of horror.