Red Bull 'Baby Cooler' repair questions

Hi, picked this up (fig1) literally on the side of the road today, compressor still runs fine but inside is like a mini oven, seriously, the back plate gets hot as. Some physical investigation has turned up a snapped thermostat line (fig2) and suspect lookin thermostat relay. Some forum research turned up that the heat is a fair indication of no refrigerant. Now with the questions.
1. Is fixing the thermostat line as simple as resoldering the good end back into the relay?
2. How does one test the level of refrigerant in the system with only a minimum of equipment?
3. If I am indeed out of refrigerant (and assuming there are no puntures anywhere) is redosing it with R134a as simple as it seems?
The diy’s have an array of methods from pro to ghetto that don’t seem too hard, or should I just take it to a guy to do for me (like a woose).

ok, any help on those would be appreciated. Help me get this thing running before i have to hide it from my wife!

Found the real reason this hit the roadside, some douche stabbed a tiny hole in the coolant plate while dislodging ice. Have patched hole with silver solder, see how we go

Assuming you can repair the refrigerant system to the point that it will hold pressure you should be able to recharge it. The hard part is that these fridges were not made to be recharged- there is no recharge fitting incorporated into the system. If you can find out what type of fitting needs to be added onto the line to allow a recharge bottle to hook up to the line then the recharge wouldn't be too hard. Good luck on the repairs! Worse case you can probably part out a few pieces and put the money towards a working fridge!

There forums were born out of a similar situation. I picked up 3 Red Bull fridges off my local classifieds for $50 and 2 of them weren't running. I looked for parts online and found NOTHING. After finding nothing I decided to pull the fridges apart piece by piece and use logic to figure out what wasn't working. Turned out one of the fridges had a bad overload compressor ($10 repair), and the other fridge needed some circuit board repair ($50 repair). After that I decided to start the forums so there would be a place to find info on these often broken fridges.

Good luck with the repair