The thing I’d worry about with a heat mat is its designed to have something on it to pull heat away. I’d worry that without something to draw heat away, it would overheat and damage itself. I might be worrying too much there, though. I use tubular heaters like this http://www.ebay.co.uk/itm/Tubular-Tube-heater-low-energy-adjustable-thermostat-bathroom-greenhouse-garage/381922947081 . While bigger, they are made for the job, often have a good thermal cut out in (though not always!) and you can normally find somewhere to mount it that won’t get in the way like a corner or in front of the bump many uprights have for the compressor. The bracket also means if it breaks, it’s easy to just replace the tube isn’t permanently affixed to the bracket. Other options might also require things being glued to surfaces in some way. The glue might not like repeated heating/cooling. I think it’s worth planning for things to break. If a heater/cable/sensor breaks, will it be easy to replace it?
The cable might work but I have never seen it before so can’t form an opinion. Having a heating element in flex like that feels like its asking for an electric shock if the flex gets caught or perishes though. I’ve never seen it in the UK and imagine it wouldn’t pass safety standards over here.
That’s the sort of power jack I meant, yes.
You might be ok with a freezer. If it’s a simple analogue temp control, I imagine you could just set it to the coldest temp and use the setup you describe. A digital temp control might try to introduce a lag after turning on or something. I’m not sure. I guess you could just try turning your freezer on/off at the wall a few times and see if it behaves sensibly
One final thing that comes to mind. Be careful of your fridge temp probe position. Don’t mount it on/close to a heated/cooled surface. That’ll result in BrewPi seeing big temp swings and it’ll over-compensate.