Electrical – Listed electric baseboard heaters that permit installation below outlets

I understand your dilemma. I have a few comments about using heated water from a wood stove to circulate in a radiator. The concept seems simple, however using a circulator pump also requires a control panel of some sort, unless you intend to let it run continuously and manually switch it on and off. This task is normally controlled by a thermostat and control board. The pumps usually run on low voltage supplied through the control board. Using line voltage (240VAC in most of Europe) and an in line full voltage thermostat would be very dangerous. Another concern would be protecting the circulating water loop from an over pressure condition. Heating water above the boiling point would be a major hazard. You would need a pressure relief valve and a way to shunt water away from the heat exchanger if the wood fire overheats the water. Another limiting factor would be that this heat source would only be available when the wood stove was burning. Perhaps you might consider an infrared quartz space heater instead of the oil filled radiator. These heaters are extremely efficient, cost a fraction to run compared to traditional electric heaters.They come in a variety of styles and shapes. The cost of these heaters start around $80.00 USD to a high of $500.00 USD depending on how large and fancy a unit you select. They do not require special wiring and have a fairly low electrical draw plugged into any standard outlet. Infrared heaters work by heating objects via infrared energy as opposed to heating and distributing air. The heat in the space is usually very even and comfortable. Check out what is available in your area.

Right. I've seen this before. Some handyman put in a subpanel, but only ran 120V service to it (who knows why - saving money on wires? Expanding one wire feeding an outlet into a whole sub-panel?) and then jumpers the hots - which works OK if everything is 120V loads - which was probably the case when the panel was installed.

This does, of course, mean that a 2-pole breaker has pretty much 0 volts across it, as both sides are fed from the same phase (both are 120V to neutral/&ground.)

You'll need to add another hot wire from the source to the panel (traditionally red in the US system - black hot, red hot, white neutral (grounded), green or bare safety ground.)

Depending what the current wiring is, and especially if it's inappropriately sized (which would go right along with the handyman's decision to run it 120V) it may be more appropriate to replace the current wiring completely with 4 wire cable (called 3-wire cable due to the convention of not counting the ground wire) or 4 wires in conduit.

I'd also double-check the status of the ground and neutral - in a sub-panel the neutral is supposed to be isolated from the ground (including not being connected to the case, which should be grounded) and I would not bet on that being how this one is, just following the pattern of behavior shown by whoever wired it up.

You should probably go over the whole electrical system looking for any other "interesting" work that's been done to it, and possibly call in an electrician to check you on anything you can't sort out. Incidentally (clarifying my comment), both QO and Homeline are fine, it's just that the breakers have to be the same flavor as the panel, and sometimes folks get the wrong one as both are Square-D products, and they almost-sort-of fit. But that has nothing to do with your problem, from your description in the comments.