Would it be possible to have a cold and remote polar region if the oceans are made of fire? By that, I mean that in the place of water, there exists lava.
Considering Earth as a template planet, probably not.
If the seas of your planet are molten lava, their temperatures would be in the 700-1200 °C. Let's assume 850 °C as an average. That is hotter than the mean surface temperature of Venus. Since lava usually contains greenhouse gases, your planet would be probably be a Venus on steroids, and its temperature would be the same anywhere.
Even if your planet didn't start out with an atmosphere (so as to maintain a separate temperature on landmasses not covered by magma), the magma itself would release gases that would make an atmosphere over geological time.
Now "cold" is relative, but the poles of that planet would not be "cold" to us.
I don't think so.
Back when Earth looked something like this:
there'd be no possibility for anything like a cold polar region. In those times, the atmospheric temperatures were something like 2000̊ C. Not really conducive to nippy polar conditions!
Several times in Earth's history, there have been flood basalt eruptions that covered large areas with lava. From memory, one of them occurred in Siberia. I don't see any reason why they couldn't occur over the poles.