About Movies

I think you were probably translating "映画について" for this title, which should be translated to "About Movies" since you're talking about movies in general; but in English we'd probably title a post like this simply "Movies"

I especially love the Jurassic World series in thewhen it comes to dinosaur movies.

Thisese movie iss are really great because of the realism of the dinosaurs, but I'm a bigger fan of

Since you're talking about a series of multiple movies, this sentence should refer to them in the plural.

Claire Dearing than the dinosaurs' realismthe protagonist, Claire Dearing.

A suggestion that, if your readers don't already know the series, it's worth adding the clarifying information that she is the protagonist of the series.
Since you've already mentioned the realism in this sentence there's not much need to repeat it.

However, at the same time, I found her lovelyappreciated her softer side, and I could tell she had feelings for Owen.

I think here you're trying to draw a contrast between her hardened side in the face of a disaster and her softer, more emotional side. In English we often describe qualities like courage, determination, stoicism, etc as being 'hard', and qualities like emotional openness, romanticism, and so on as being "soft"

About Movies

About a Movie = a specific movie
About Movies = movies, in general

I especially love the Jurassic World series in the dinosaur movies.

This movie is really great because of the realism of the dinosaurs, but I'm an even bigger fan of

Claire Dearing than the dinosaurs' realism.

This rephrasing is a little more natural, but your original phrasing got the point across well.

in front of an overwhelming predator, and I was really drawn to her.

Since this "a" comes before a word that starts with a vowel, it should be "an" instead.

However, at the same time, I found her lovely, and I could tell she had feelings for Owen.

There's nothing really wrong with this sentence but I wanted to point out it's nuance because I'm not sure if you meant it this way.
When you say, "at the same time", referring to something else that you said earlier, it usually has a contrastive feeling to it, and you feel that both points are true, even though they contrast each other.

例文：
I've heard that Steve Jobs was a jerk to many people working at Apple but, at the same time, he accomplished many amazing things during his life.

About Movies

When it comes to dinosaur movies, I especially love the Jurassic World series in the dinosaur movies.

"When it comes to ..." is a nice way to introduce a category or genre.

Thisese movie iss are really great because of the realism of the dinosaurs, but I'more than that, I am a bigger fan of the character Claire Dearing.

When discussing a series of movies, you want to use plural forms.

Claire Dearing than the dinosaurs' realism.

Moved this sentence into the sentence above

It seems that she hads both prosgood and conbad qualities.

Another way to write this: It seems that she is a complicated character.
Pros and cons is a little strange when talking about a characters personality. We use pros and cons to discuss plans or decisions.

As the CEO of the theme park, she facedhad to deal with chaos when the dinosaurs escaped.

She ran in high heels and showed the ability to take action, remarkable judgment and courage in the face of an overwhelming predator, and I was really drawn to her.

in front of a overwhelming predator, and I was really drawn to her.

combined into the line above

However, at the same time, I found her lovely, and I could tell she had feelings for Owen.

"However, at the same time" is strange here. In the previous sentence you discussed a good quality (courage, judgement, etc.) and here you are discussing another good point. "However, at the same time" is used when discussing points that are different or don't "agree" with each other.
for example:
I like horror movies, however, at the same time, I am afraid of them

When I watched the movies, and for a while I felt like I had become Claire.

Movie series, so we want to talk about this as a franchise/more than one movie.
"When" is more natural here when talking about a temporary feeling.
When I went to Rome, I felt so happy. (but now I am not)

Anyway, even from the point of view of women, I’m pretty sureEven from a woman's point of view, she is charming.

About Movies

I especially love the Jurassic World series in theof dinosaur movies.

Another way to write this sentence: "When it comes to dinosaur films, I especially love the Jurassic World series."

Thisese movie iss are really great because of the realism of the dinosaurs, but I'm a bigger fan of

You mentioned the Jurassic World series and not a specific movie, so I changed it to plural form.

It seems that she had both her pros and cons.

As the CEO of the theme park, she faced the chaos when the dinosaurs escaped.

She ran in high heels and showed ability to take action, with remarkable judgment and courage

in front of an overwhelming predator, andso I was really drawn to her.