1. A physical quantity is something that is real. I can show you ten apples, but I cannot show you ten seconds.
I believe that it is indeed entirely correct and proper to refer to time as a "physical" quantity. Same with space. Apples can be
seen, but that does not make them more "real" than something that cannot be seen. The wind cannot be seen but it is clearly real. I am not entirely what you mean by "showing" something, but I do not think it is a good criteria for establishing physicality.
I suspect that you believe that time is some kind of immutable, unchangeable "thing" that, in a sense, "sits outside" physical reality. I suggest that such a view simply does not square with the observational evidence.
Time, of course, is a tricky concept. But whether it be the hands of clock, the oscillations of some nuclear particle, the sequence in which two particles decay, or whatever, one thing seems pretty clear - the way these "mechanisms" mark time is influenced by gravity. So this is pretty powerful evidence that time itself is being affected by gravity.
Consider the twin paradox. From wikipedia:
"In physics, the twin paradox is a thought experiment in special relativity, in which a twin who makes a journey into space in a high-speed rocket will return home to find he has aged less than his identical twin who stayed on Earth."
Now there are lots of things one could say about the paradox, but for our present purposes the following should be noted. All physicists (or at least the overwhelming majority) believe that, indeed, the travelling twin will return
younger than the one who stays at home.
The travelling twin will look younger, he will feel younger, he will have less grey hair, more strength, etc., etc. The point being that,
compared to the earthbound twin,
all the physical processes in his body will have slowed down.
Do you not see how this suggests that, for the travelling twin,
time itself has slowed down. Sure, the travelling twin's watch will also show an earlier time than the watch on the arm of the earthbound twin. But relativity has done more than slow down the watch, it has
slowed down the very biological processes in the travelling twin (at least relative to the earthbound twin).