Day old coffee does still have caffeine.
The caffeine in the coffee does not evaporate no matter how long the coffee has sat out.
Plain black coffee can sit out at room temperature for more than 24 hours after brewing. It will still be considered safe to consume, though its original flavor will be lost.
On the other hand, hot coffee with added milk or creamer shouldn't be left out for more than 1 to 2 hours.
Overnight coffee is safe to drink and you can reheat it in the microwave.
It is OK to microwave coffee.
Microwaving coffee is perfectly fine and I do it myself everyday.
However when microwaved the coffee is not as good as fresh brewed coffee is and it can become strong.
When microwaving coffee you should add a bit of water to dilute the coffee so it does not get as strong when reheated.
I usually have a half pot of coffee leftover by night and then leave it out overnight in the coffee pot.
Then I add some water to the coffee pot coffee and then pour it in a ceramic coffee mug and heat the cup of coffee in the microwave for 1 minute and 30 seconds.
Reheating coffee is not bad for you.
Depending on the brewing method, your reheating method, and any additives in your coffee, you will change the taste.
However, there are no bad health effects of reheating your coffee.
Reheating your coffee is fine but expect your coffee to lose its original taste.
The microwave breaks down the aromas which are the key element for giving coffee its flavors so the salt, bitter, sweet, and sour tastes that you taste in your cup.