When would you use 'heureuse' as opposed to 'heureux'? Is it a m/f thing? Because one cannot tell from this sentence.
It's a m/f thing, but they're also pronounced differently in this sentence. The "x" at the end of heureux would be silent here, but the "s" is pronounced in "heureuse".
Is there a difference between bonheur and heureux/use? The both seem to translate as "happy".
Bonheur is a noun - happiness. Heureux is an adjective - I am happy
Is there a reason " I am very lucky " is not a correct answer here or is it just an oversight? I could see given context, where this might be incorrect, but on it's own I see no reason why it can't be translated this way.
Generally to be lucky would be translated using 'chanceux'. i.e. Je suis très chanceux. Or, you could also say 'J'ai de la chance' - I am lucky. 'Heureux' can be used when talking about luck if you are referring to an expression such as 'lucky shot', where you can say 'coup heureux'