Because that's not very good English. You need an adverb here, and 'good' is not an adverb, but 'well' is.
You can have a good person, good journeys, or do a good deed, but if you're doing something in a skilled fashion, you're doing it well.
"At gøre" is usually translated with "to do", i.e. working on a task. "To make" is usually "at lave", which rather refers to creating something.
Isn't the combination of meget and godt something different, meaning more in the direction of quite well?
I don't agree. Depending on the context, it could also mean "pretty well". But it would normally be suggested in the tone of the sentence if it means very well, or pretty well.
How do you know if it is 'that', 'the', or 'it' that is used in the sentence??
Det can only be translated as "the" if it's followed by an adjective in the definite form (e-form) and a neutral-gender noun: det røde bord - the red table. Sometimes the noun can be implied: "Der er mange ord skrevet her, men det røde er vigtigt." - "There are many words written here, but the red one is important."
If the det is rather standing separately, it can either mean "it" or "that". "That" can also be more ephasisedly expressed with det der - that over there.
Or you could go for what makes grammatical sense in English. "She has done the very well" doesn't make a lot of sense (unless you take some grammatical liberties and are talking about a physical well, which would be translated as brønd in Danish). "She has done that/it very well" is better.