Are sense objects objectively real? Do they continue to exist while we're not perceiving them? Philosophically I think "real" would equate to realism.
There is absolutely no way to know.
Sure there is. Just reject the skeptic's warped view of knowledge.
Let's discuss light as being the sense object associated with the eye. A photon (particle) of light which acts as a sense object enters the eye and interacts with the sensitive part of the eye and along with eye consciousness produces contact. It seems that you are saying that the photon continues to exist after the perception it took part in has ceased....but what is happening from a worldly view is that the photon has been absorbed by an electron causing the electron's energy level to increase and the photon just disappears and no longer exists....in other words the photon of light actually ceases to exist after it is perceived.....seems to disagree with your view.