Have been penalised so far for using house instead of home and visa versa. Does context specify whether it is home or house?
No, it honestly doesn't. Please report the error so that the admins can fix it.
Is there an appreciable difference between "She reads THE newspaper..." vs. "She reads A newspaper...? Can the sentence be read either way?
Considering that the program hasn’t consistently distinguished between the indefinite (a, an) and definite (the) articles so far (which are sporadically used in conversation anyway) I think it’s nit-picking to count “THE newspaper” as incorrect
As many sentences are without context, it would indeed be interesting to find out why 'the' cannot be used either. If you regularly read the same named newspaper, it would be perfectly normal to use 'the'.
Dia means she/he though so you shouldn't be penalized. Now if the sentence was something like "Dia adalah raja kami" and you said "She is our king" then I would understand the penalizing there.