N-MOSFET switching behavior when turning off
You have a massive loop inductance in your measurement set-up: -



I've tried to indicate that with a green dotted line showing the loop. I estimate that loop inductance to be about 1 uH. If I simulate a 1 ohm load in series with 1 uH I get this: -




Vin (red) is the gate drive voltage (fed via a 10 ohm resistor but could be made much worse by having long leads as indicative of the set-up picture).
Vout (blue) is the drain voltage
i(R1) is the current through the 1 ohm load


I'm using an IRFZ44N MOSFET by the way - the same as shown in the OP's circuit diagrams.


  But then why is there that big rise on the battery voltage?


Because of bad probing techniques and an ill-defined 0 volts node (also with series inductances). Just look at the grey left-most probe tip connected to the red lead from the battery - that probe earth point is back close to the source of the MOSFET but, there's a hundred mm (or more) ground wiring back to the battery negative terminal so, it's impossible to conclude that there is any movement on the battery voltage at all. Everything need to be ten times closer to make any sense of o-scope readings and even then, there'll be ringing and inductive artefacts present (but smaller).

And, I haven't modeled the inductance of those power resistors - you can get low inductance versions of those resistors but you appear to be using the standard parts and the data sheet doesn't give any indication of the inductance for those parts unfortunately.