The "bad guys" (I assume we're talking about government types) can park outside your house or just lean on the electric/gas company for that info already. Or considering how some people broadcast their location with Twitter/Foursquare/Facebook/Etc, just watch that.
Parking outside your house requires that they have enough interest in you to dedicate resources to the task. The electric/gas meter in your house is not literally designed to detect when there is a human home and when there is not.
Nest really isn't great for that either, aside from what I'd call an adaptive timer based on how you adjust it.
But if you have access to someone's live power usage, you probably have a good idea of their schedule. On top of that, your phone makes a much better tracker than your thermostat.
Depends entirely on where it's located in your home. I've tried and sold a Nest because my home thermostat is upstairs, and the only thing upstairs are bedrooms. During the day, there's nothing to trip the sensor.
Your phone makes a much better tracker for such things.
What did you replace it with? The nice thing about connected devices is that, well, they're connected. My Nest is also not somewhere I typically walk by during the day. That's alright, I have a $10 motion sensor in another room I do use, and in 5 minutes set up a rule on my home automation hub that sets my Nest to "home" when that sensor is tripped. That's only possible since Nest is internet-connected and has an API.
Nothing equivalent. I just replaced it with the standard programmable timer thermostat that was there before I got the Nest. It was partly the fact that the presence detection wasn't working for me, and partly the fact that I had a sudden cash flow problem and was still within the return window :)
I haven't invested the time into setting up a proper home automation rig yet, but it is on my to-do list.
