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First off, I sent my phone while it was under warranty and still is to be fixed since the screen backlight just died I can't see anything. They returened it back to unfixed due to "Damage beyond repair" and the warranty will be void. Now I have unfixed device and sony voided my warranty and they won't replace it whatsoever.
Is it mentioned in the warranty terms and conditions that if the repair cost exceeds the value of the handset then the warranty will be void?
According to 8558068464 (Sony Help Center), yes.
Hi @Hassani, sorry to hear about this. 
I'm not very familiar with the service routines in North America, however in the market where I'm situated (the Nordics) the warranty will be voided if you for example, modify the software in the device, or if you have used a third party repair solution.
Based on what I can see on the form you uploaded, it says that the device out of warranty because of damage that is not covered by our warranty.
For more information on the repair and more clear information on the warranty terms/service routines, please get in touch with your Local support team and they will assist you further.
Keep us posted!