We'd never say that in English
would't wall be כותל?
It is a very formal word but yes.
why would a wall be dyed rather than painted?
The sentence uses the word "paint" but perhaps the alternative answer is "dye" because that was a frequent report by many people. Probably not though.
Definitely should be 'we are painting the wall'. Unless there really is something unusual being done to change the colour of the wall....
we are painting the wall