I'd just want to know if it's possible to supply a common mobile phone with a 2 wired 3.7V Li-po battery like this one instead of its proper Li-ion battery, eg this one.
If yes, how?
I suppose so. First thing will be to go there:
http://www.cpkb.org/wiki/Nokia_BL-5C_batteryAs said above, you need to connect a 82k resistor between the BSI pin and ground to emulate this battery. Second thing is that the original battery is about 1000mAh, whereas the one you pointed to is half of that. Third thing is that the original battery is very likely a Li-ion battery with a 4.1V max voltage, as opposed to 4.2V for a typical LiPo battery. Note that in this direction it should not be an issue, the internal charger will just not charge the new LiPo to its full capacity. But I'd suggest getting a similar capacity so that battery life will be similar, and the charging current will be adequate. Also, with half the capacity, the phone will probably not estimate the state of charge properly.
So, get a 1000mAh battery to begin with.
Other than this, I think it has good chances of working. Those "old" batteries did not contain electronics with identification (along with a fancy connector), as more recent batteries do.