Can daily consumption of green tea (I mix it with black tea as well) increase chances of getting kidney stones? The tea is unsweetened.

Probably not. There's a "pop" claim that tea and cola predispose to kidney stones, but little scientific reason. The overriding key to prevention is to keep the urine dilute (always pale, never dark) by drinking plenty of fluids -- the cheapest is tap water, and perhaps tea-drinkers are actually just drinking less of that.
Not likely. I did read a strange report of someone who got kidney failure from stones from drinking black tea...about 2 GALLONS a day! Apparently oxalic acid. So just don't overdo it! But tea in general, ESPECIALLY green tea, are very healthy and especially if you don't use sugar. Good health to you!