"This woman drinks a lot of wine."
Translation:האישה הזאת שותה הרבה יין.
the she isn't grammatically possible in English. (or any the + pronoun)
You mean *הרבה יין, and yes, the former would make you sound ridiculously pretentious.
This is not a form of רַב (root רבב), which you put after the noun, like in יַ֫יִן רַב "much wine", but the adverb הַרְבֵּה, which you put before the noun and which cannot change its form. Etymologically this is the absolute infinitive of הִרְבָּה "he increased" (root רבה)