[Grammar] Capital punishment vs. Death penalty (article question)

[shimacatu_sa]

[FONT=.SF UI Text][FONT=.SFUIText]Hi, [/FONT][/FONT]
[FONT=.SF UI Text][FONT=.SFUIText]I took some grammar quizzes on articles provided on this website today and found the following answers confusing to me.[/FONT][/FONT]

[FONT=.SF UI Text][FONT=.SFUIText]Q17. I am against ( ) capital punishment. (no article)[/FONT][/FONT]
[FONT=.SF UI Text][FONT=.SFUIText]Q24. I don't believe in (the) death penalty for any crime. (definite article)
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[FONT=.SF UI Text][FONT=.SFUIText]I believe that capital punishment is an uncountable noun, and death penalty and death sentence are countable. However, a definite article is used for death penalty and death sentence in most cases because these cannot be given more than one at sentencing. In other words, everyone is definite about the death penalty /sentence.[/FONT][/FONT]
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[FONT=.SF UI Text][FONT=.SFUIText]Am I correct ? If I am not, could someone give me guidelines for making the right article choice in this case ? I have a basic understanding of English article use, but I am still struggling with using articles.[/FONT][/FONT]
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[FONT=.SF UI Text][FONT=.SFUIText]Are the following sentences grammatically correct ?[/FONT][/FONT]
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1. [FONT=.SFUIText]A judge gave the defendant the death sentence.[/FONT]
2. [FONT=.SFUIText]The defendant was given the death penalty.[/FONT]
3. [FONT=.SFUIText]The judge gave the defendant a 90-day sentence.[/FONT]
4. [FONT=.SFUIText]New York State doesn't have capital punishment. [/FONT]
5. [FONT=.SFUIText]He was given a life sentence for the murder of his sister.[/FONT]
6. [FONT=.SFUIText]The death penalty can be a controversial subject.[/FONT]
7. [FONT=.SFUIText]Capital punishment can be controversial.[/FONT]

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[FONT=.SF UI Text][FONT=.SFUIText]Thank you.[/FONT][/FONT]

 

[Rover_KE]

They are all correct.