Simplified answers to your questions are.....
The easiest way to check if your 4x4 is working in H4 is taking it to any workshop with lift, raise the vehicle, in H4 all 4 wheels should rotate equally.
Leaving the wheel hub locked minimally increases your fuel consumption, and also very slightly more wear n tear (because you are turning the front drive shaft all the time) but it does no damage. Leaving the wheels hub lock unlocked or in free position means, your front wheels are not connected to diff, so even with H4 or L4 activated even though your transfer case is providing power to front drive shaft and to front diff, but your wheels are not connected, so you won't have a working 4X4.
For normal driving the overdrive button should be left ON.
I may be wrong, but the tyre sizes mentioned in your post do not appear usual sizes. Could be a typo. Common size for Prado is 265/70R15,. And also the replacement size mentioned is probably 285/75R16 (285/70R16 is very uncommon)