are single pane windows illegal?

Not illegal, just not effecient. The plastic film and tape makes a big difference, creating a second pane.

Not only are existing single pane windows grandfathered in, but they are still legal for purchase for garages and storage buildings.  There is no requirement for upgrade for most dwellings.

Yes, electricity costs about 4 times as much as natural gas for the same amount of heat energy.  But you can heat just selected rooms, and there are multiple ways to minimize heat loss at windows.

It is not just the glass; one needs to check the seal at the edges of the windows (and doors) too.  Sometimes caulking helps.  Other times the foam insulation is needed to allow windows to still open but seal when closed.

Black out shades help quite a bit.  Heavy draperies help even more.  For lower costs, one could just use blankets, or even just a couple sheets stitched together filled with crumpled newspaper.

If one is careful at monitoring the window shades, one can get the benefits of natural heating from the sunlight during the day, and can seal the heat in at night.

And one can always wear more sweaters... indoors as well too.

As for the heater that went out...  for gas heaters, my experience is that about 60% of the time it is just dust that needs to be vacuumed out.  And about 20% of the time it is just a lose wire for the thermostat (or in some cases a bad battery on a newer thermostat, or occasionally something broke internal to the thermostat).  About 10% of the time the pilot just blew out from a draft or something else (such as a flood in the basement...) and just needs to be re-lit.  About 5% of the time, the thermocouple has gone bad and either needs to be cleaned or replaced.  And about 5% of the time, the gas valve has gone bad or something else.

Anyway, in most cases the existing heater can be functional in just a couple hours of checking and correction.

I hope you get the regular heater repaired soon.   Of course, December was much colder than November in Oregon, so the bill would have gone up anyway.  

When I lived in a rental with single pane windows, we used the plastic window covering to make a double layer.  (Yes, it was our expense, but it made it much more comfortable).

No.  They may not meet energy efficiency codes for new construction, but would be grandfathered in on existing houses. 

The portable heater might possibly be a code issue if it is being used as a permanent solution for heating either for code or the terms of your lease.  You would have to check with the city or county for rental property heating requirements codes, it is possible that the current heater satisfies those requirements as well.