1.) Is it possible to use a single HM-10 with an Arduino Uno to read from a sensor and send to an Android application while also being able to send data from the application to the HM-10?
Yes and Yes. Read the HM-10 Manual to get an idea of how. Implementing it will be a bit of work. This response is to help you get started in solving your problem, not solve it for you.
Good Luck & Have Fun!
Gil