That temperature range is fine for this model. The only thing is that you'd have to manually set the switch to Heat and Cool depending on you what you need in the house. That setting is not automatic. So for the winter season, set it to Heat. For the summer season, set it to Cool. Hope that helps.
Both! You can set it to change automatically between heat and cool, or you can force it to change to whichever one you want. I've always done it manually, because such a changeover often occurs when the temperatures outside/inside don't require EITHER heat or cool, so I just wait until I feel the need for heating or cooling. Hope this helps.
I don't think it has a lock, although I have never looked asi don't need one. I am pretty definite I haven't seen any humidity readings. If I was a gambling man, and I have programed mine several times, is answer no to both of your questions.
My old thermostat had to be switched from heat to cool. The Hunter works perfectly in this application (gas furnace plus air conditioner). If you have a complex system such as multi-stage or heat pump, I'd consult with an expert.