#1 The c1's back is black in pictures but fully white in unboxing videos. how can i purchase the black version? rear panel lottery...?
The C1 series sold in the US has a black back cover. However, some other markets will have white so it's possible that any unboxing videos you've seen were done in other markets, where a white version will be sold.
#2 What’s the difference between ‘wall mount’ and ‘can be wall mounted?’ Can all these TVs be tabletops?
'Can be wall mounted' should mean that the TV comes with an attachable stand but you could wall mount it instead if you get yourself a wall mount, while 'wall mount' suggests that the TV does not come with any stand. This TV does come with the wide solid stand shown.
#3 I'm planning on using this as a computer monitor. Is burn in still a problem or has it been fixed?
Don"t think it's fixed should be alright if you don't leave it on the same screen for a long time.