(Part One)

1. The producer of the distinct movie blockbuster took for a long time to refine it.

(Something "distinct" is different in some way from the others in its class. If you are referring to a good movie that is well-made and successful, perhaps you can use the word "blockbuster". / You do not need the preposition "for" with "took" in your sentence. The producer "took a long time", not "took for a long time".  Having said this, there are expressions where "take/took" are used with "for": "take for granted". Example: Do not take for granted (assume) that the deal is still on after this meeting.)

2．The play is slated / scheduled to premiere next Saturday.

(Alternatively, we can use "scheduled" to refer to an event that is planned to take place in the future. Example: Flight SQ216 bound for Taipei is scheduled to depart at 7.30 p.m.)

3．It is hard to understand the genealogy of the heasan due to the terminology used.

(I am afraid that I do not understand the word "heasan". Is this the name of a certain tribe or a group of people related by blood and living in a certain area? If it is, "Heasan" is a proper noun and the first letter "H" should be capitalised: the Heasan(s).)

4．He was courted persuaded by the villain to commit a crime.

("Courted" would not be an appropriate word as it would mean that someone is trying to treat you nicely in order to win your love and affection. I would suggest using "persuaded" to mean that someone is trying to get you to do something by providing you with reasons. "Convinced" is slightly different from "Persuaded". "Convinced" means someone has made you believe in their opinions and views. Someone has to convince you of their cause before they can persuade you to do something. Example: He convinced me of the importance of having an insurance policy and persuaded me to sign up for the one with the highest premium.)

5．The prolific writers' works are imbued with a spirit of love.

(You would need an apostrophe to indicate that the "works" are creations of the writers, and are considered to be the writers' possessions.) 

I hope this helps.

Could you check my sentences, please?-5

If there are mistakes, please correct them.

1. The producer of the distinct movie took for spent a long time to refine editing it.

-distinct is a weird word choice here. Not sure what you mean.

2．The play is slated to premiere from next Saturday.

3．It is hard to understand the genealogy of the heasan due to the termiology.

-“heasan” is not a word. Not sure what this sentence means.

4．He was courted convinced by the villain to commt commit a crime.

-Probably more typical to see “the villain convinced him to commit a crime” but both are correct.

5．The prolific writer’s works are imbued with a spirit of love.

-a technically correct sentence, but sounds a little silly.

6．The government is trying to allay their fears about the calamity and the chaotic situation.

-technically correct, but would be better to define “their” ex “the government is trying to allay the people’s fears about the calamity and chaos.”

７．He gave her some adornment under the table to change her mind.

-wow this sounds dirty haha. Adornment is definitely not the right word, but not sure what you were intending to say here.

8．The company gained prominence by unification of subsidiaries.

-technically correct, but not sure of the meaning. Prominence is being well known. 

I really appreciate your attention!

Etsuko

Overall, I think using less complex words will aid you in getting your point across. The sentences seem like they are relying on a thesaurus. Hope this was helpful!