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 the first sentence is in possesive form.

 [onların] rezervasyonları ---> their reservation [their booking] 

literally,

there is their reservation in this restaurant. 

Bu lokantada rezervasyonları var 

therefore we can´t get rid of plural. It has to be in plural.

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In the other sentence you dont have to put plural ;

 They have booked this restaurant --> Onlar bu lokantada rezervasyon yaptı.

* but we have to mention the pronoun [onlar] to be able to make the verb singular. 

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Bu lokantada rezervasyonu var. is again in possesive form, noun sentence.

He/She has his/her reservation in this restaurant.

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I know, Yarvik.  

Bu arada [by the way] , In Turkish One could also say ;

Onlar bir otel ayırttılar. ---> They booked a hotel. 

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In the previous sentence the logic is , "they have a hotel reservation" which is what we call "noun sentence" and therefore we use possesive form. That´s why I gave the literal translation of it for you to understand. 

They have  their booking  in this hotel.