1997 Porsche Boxster died while driving.

[blue62]

The hose in your picture is the coolant overflow hose.
So with the engine overheating the hose is doing what it is supposed to do.
Venting expanding coolant.
The best way to diagnose coolant systems issues is with a coolant system pressure tester.
Harbor Freight has them for reasonable price.

Sounds like either your coolant overflow tank, the bleeder valve or the coolant cap is toast.

Your P0117 code is telling you that the DME/ECU is not getting a signal from the coolant temp. Sensor.

When you do get it started and running at higher RPM does it run smooth or rough????
What is the Lowest RPM you can keep it running at? and how does it run?? smooth or Rough.

Doubtful that it is a fuel pump issue.
If a fuel pump cannot supply enough fuel at low demand=idle... it is very doubtful that it can supply enough fuel at higher demand.
As when you give it gas and it runs.