You can purchase an O2 bung to weld into the exhaust pipe rather than
just a nut.  1.9 engines have the O2 sensor well forward of the cat in
the J pipe.

If you have no O2 sensor connected (and its connector isn't grounded)
then it shouldn't run differently at the point that it would "Normally"
go into closed loop unless 1., the shielded wire that runs from the ECU
to the O2 connector is shorted, or 2., the Temp II sensor or its
connector or wiring is amiss.

As to the difference between generic O2 sensors and the prewired
sensors, I couldn't tell you.  I use the generic ones in my 1.9s and
they seem to do the job.  I did get one bad one once.  It was "New" but
caused the engine to run badly when it went into closed loop.

Mike