While correct, it sounds very out of place here. "I do not take any medication" would be the most used/heard answer. "I do not take any medicines" sounds (if you'll forgive me) like a non-native speaker. "I do not take any medicine" would sound less strange. Medication and medicine are two of those weird English words that can be spelled in the singular, but represent plural. If someone said "I do not take any drugs", the assumed meaning would immediately be that they are talking about pot, cocaine, hash...etc.... They would want to throw in "prescription" into the sentence. "I do not take any prescription drugs".
Whether you say medicine/medicines or medication depends on where you live. Medication is not used commonly in the UK or Australia. There medicine or medicines is more usual and either can be used as the plural. Similarly, while "drugs" usually refers to illegal substances, among younger people in Australia at least, it's not uncommon for someone say they want drugs if they're not well - as in "I've got a headache. I need drugs." meaning an over the counter painkiller or a prescription medicine. It comes down to context and most people would not add "prescription" because it would be obvious they weren't referring to illegal drugs and therefore "prescription" is unnecessary.
In the US, "medications" as the plural is pretty common. For example, if you go to the doctor for an annual physical, s/he will routinely ask you whether you are taking any medications.
"Medicines" is much more unusual. I wouldn't go so far as to say it would make someone sound like a non-native speaker, but it is much more unusual.
I like your translation. I suggested "I do not take any medications at all" a year ago and I got a notification a few days ago saying it is accepted now! It takes a while sometimes because of all the ones they have to sort through but you still should try and suggest. Did I mention I finished the German tree a few days ago? Yay me! :-D
No, it sounds very weird. You could say "Ich nehme Medikamente nicht." (maybe when you're echoing a phrasing in a question, for example) or "Ich nehme nicht Medikamente, sondern (etwas anderes)." (i.e. this would only work if it's contrastive). But "Ich nehme keine Medikamente." is by far the most natural phrasing.