The boards look OK but the 5th image seems to suggest a faulty backlight Led or Leds given the dark shadow so perhaps the burning smell may have been one failing and then overheating and melting part of the plastic diffuser but this is just a guess.
The black vertical line could be a tab connection fault This is the ribbon cable(s) connection onto the LCD panel itself and the cable lifts off the panel hence the black line.
Both problems seem to be with the screen i.e. backlights and cable connection from the screen itself.
You could check to see if a section of the cable in line with the vertical black line has lifted (only a small section would have lifted) and check if you can tape it back down and still maintain electrical contact between the cable and the panel. It is a very fragile connection so take it easy.
Here's a video that may help. I couldn't find one for your exact model but generally they're the same.
You can see the tab cables (aka address board cables) at 10:07 minutes in.
Also remember which way the diffuser sheet comes off so that you put it back on the same way and not back to front.
Backlight strips (example only) for your model are available online. Just search for Ue55ku6400u backlight strips to find suppliers that suit you best.