What is the ruling on a fasting person using mouthwash, gum medicine, teeth whitener, toothpaste, lemon, or a miswak during the daytime in Ramadan, without introducing anything into the stomach?

Using the miswak is a recommended Sunnah at all times, and this includes daytime in Ramadan, whether the miswak is used at the beginning or end of the day, or whether it is a wet miswak or otherwise.

As for toothpaste and mouthwash, there is no harm in using them if one is certain that they will not reach the throat or that nothing will be swallowed. However, it is preferable to postpone their use until after breaking the fast.