yeah you really need to put a scanner on the car and watcht he 02 values. not sure if the AP has the capability. i doubt the 02 sensor would be the cause of the fuse blowing.You're not going to be able to test an o2 sensor with a volt meter thet are very tricky to test....
You described the exact same problem im having right now with my 2011 wrx sedan. Just installed a turboback 3 weeks ago... and a few days ago threw p0031 and p0037. Can runs like dog crap... fuel economy is terrible. Jacked up the car yesterday and found frayed wires on the rear O2. Blowing fuses as well. Ordered a new front O2 sensor from Rock Auto.It may be the sensor, it may not. It may just be a short in the wiring. Check to see if you damaged any wires putting your uppipe in. If you don't mind wasting another fuse. Try putting one in with the o2 disconnected. Then you can isolate the problem.
You also may have a problem with the rear as well. So check all those wires for any damage.
Driving around this way will probably ruin that front O2 sensor if it's even ok now. Without the heater the sensor won't last long. Most likely the car will stay in open loop fueling and the ecu will not be able to make changes to AFR. I would certainly stay out of boost. Biggest hit will probably be fuel economy.