Is there in existence any set of physical parameters which can be measured, which would enable one to determine whether or not reality by itself is a dream?
No, this is impossible. Any measurement made would have to be interpreted by a subjective experience that is subject to manipulation by one's dream.
Yes. Take a glass full of water and let it fall and shatter on the floor. Pick up the glass and drink the water. If you can do it, it's a dream. If you can't, it's reality.
This article offers a possible answer - meditation should be possible even in a dream that isn't recognised as such, and lead to being 'more awake' by observing the minds operations on the world vs the world presented by our senses https://www.huffingtonpost.com/entry/a-buddhist-sleep-lesson-a_b_428653 In this Buddhist perspective there is more and less dream-like, and this can be observed subjectively.
Lucid dreamers talk about things like digital displays and the operation of light switches being giveaways - though it sounds like there is a lot of variation between dreamers to me.