For example, if one were to ask in Mandarin, 'Make sure you're drinking tea every day,' or 'You should be learning Mandarin first,' how would one respond if they are doing these things? Simply '是'? Or '喝' and '学' respectively? Or something else?
These questions fall under the category of "exhortation". In Chinese culture, the most orthodox response to exhortations is called “有则改之，无则加勉”, i.e., just agree that these exhortations are helpful and you'll do it, without emphasizing that you're already doing it. So in most cases, the answer is “好的” or “明白了”. If the other person has a higher status than you, or if you are begging him to help you, this answer is often the only and most respectful option.
If you really want the other person to understand that you are already doing these things without his re-emphasizing, there are no short answers in Chinese. You have to explicitly state “在做了在做了” or “不用你说我也知道”. However, such an answer is rude and slightly offensive, and the other person will think you're implying that he's talking worthless nonsense. So don't say this to someone higher than you in a formal setting, unless you just want to be offensive, or the other person is close to you.
To complicate things more, if you really want the other person to know you're already doing it, and you don't want the person to feel offended, you need to be longer and more euphemistic. For example, “感谢您的提醒，其实我已经在这样做了，不过还是感谢您。”
By the way, a single “是” in Chinese usually means "your statement conforms to objective facts" rather than "I will do as you say". Only in the military do soldiers answer an officer with a “是” to mean "I will do as you ask".
A: "Make sure you're drinking tea every day," - 你記得每天都要喝茶，
B: "I do (drink tea every day)" - 我有(每天都喝茶)
A: "You should learn Mandarin first" - 你应该先学普通话
B: "I did (learn Mandarin first)" - 我有(先学普通话)
A: "You should be learning Mandarin" - 你应该学普通话
B: "I am (learning Mandarin)" - 我有(在学普通话)
content in the ( ) can be omitted