Chosen Solution

Hello, Was changing screen and forgot to disconnect battery( So, looks like backlight diode/filter is burned, but also when you connect battery, place where you connect screen on logicboard is becoming very hot in like 15-20 sec and there is burning smell. What could get iphone heating up so quickly even when no screen is connected and is there any point to try and fix it?

Sounds like more than the backlight filter getting shorted, you may also have a shorted backlight driver chip. Anyway better to leave the battery disconnected for now and take it to a reputable shop that does microsoldering to get the backlight circuit repaired. Good ones have a no-fix no-fee / no-charge repair model.