the display on the phone went blank by itself without broke screen

Almost black but not completely?

OK, First try a Forced restart

https://support.apple.com/guide/iphone/force-restart-iphone-iph8903c3ee6/ios

If no better then you need to make sure the brightness is turned up in settings or the control centre. Go into a darkened room if necessary.

After that arrange a repair. 

https://support.apple.com/iphone/repair/service

the costs of the repair are borne by me?or will apple do it? My warranty has recently expired, but I have read from your consumer rights that I can apply for a hardware replacement, repair or supply of parts that require repair. is it true?

If you mean the "fix it yourself" announcement, that applies, as far as we read, next year, initially for iphone 12 and 13 only.

In your case you pay for a repair out of warranty according to the schedule I linked to.

You didn't mention the lines on the screen before.

= Hardware failure.

Arrange a repair. 

https://support.apple.com/iphone/repair/service

My glass screen is not broken but my display start going crazy, it starts from left side on top of the screen and after go on whole screen. I didn’t do anything to broke it, touch is working as well