Yes, Donna, it ("it" specifically being this item: Suburban NT-12SE Furnace Thermostat
) does indeed have a positive shutoff - at the left end of the setting lever's range there's a detent where it goes to a solid "off". (The old one on my trailer had a separate switch on the bottom for that, hand-labeled in black Sharpie for "ON" and "OFF" by a previous owner - not so stylish and another reason for upgrading.)
The new one's temp control isn't calibrated in degrees like the old one was, although I don't think that was very accurate anyway - seems to me like the position of the new one's lever corresponds pretty closely to the old one's for the same temperature, and I don't find it to be a problem to not be able to set it by a temperature scale - I start out with it about in the middle and if it's too cold I turn it up, too warm I turn it down. The built-in thermometer seems about the same, too.
I don't recall whether the mounting holes were an exact match or not - I think I may have had to redrill one of the two holes a very little bit over from the old one. Wasn't a problem, anyway. (My Scamp used Phillips screws and not rivets here, I don't know whether that's typical or not.)