can i just ask what is wrong with splicing in the 2 different connections?
ie. you said about the alternator
just keep the 1.6 alternator, but cut the non fitting connector and splice in the correct one, lining up the correct wiring
in all honesty a p10 loom and ecu would be your best bet any ways (depending what the engine came from, again best with a p10 engine) but any ways such as lights (i think i seen lights) it is just a matter of splicing on the correct wires on the loom to the correct connector (or change to golf headlights as they the same connectors as the k10 (~think k11 aswell)
the battery light coming on your dash means that the battery is not charging (defunct alternator or the fact that it not wired up if you hadnt wired it up at the time)
seems to me like there not that much to sort really to get it running fine!
admittadly wiring loom is the hardest thing to do if you r not sure on what your doing!
but best bet is find a p10 wiring loom both sides the engine side and the clocks side!
get printouts of BOTH the k11 wiring loom setup and the p10go through the k11 marking up which connectors goes to what object in the car (ie, alternator, starter, injectors, blah blah) and do the same on the p10
go through them both marrying up both sides (so log what connector on the k11 that goes to the alternator and log the one that the p10 uses, if they different then put the correct one on the wiring loom your gonna use, i advise using the p10)
simply wiring diagrams as MOST parts (alternator, starter, battery all run on the same principle wiring structure, just maybe with different wiring colours etc but they all have the same principle wires) marry these wires up to the correct connector you shall need, the only thing k11 that you would need would be doors/lights etc that you are keeping k11
engine side of things you want the engine wired up with the correct loom p10 engine to p10 loom for instance and this goes directly to the p10 ecu (non nats this way) then you will have a p10 wiring loom that all you need to do is splice in k11 lights connectors/door wiring blah blah....
could easily do a wiring loom in a night. maybe 2, aslong as you prepare yourself properly with printouts of both looms so you can trace them to the place they need to go
hope this helps, and hope you carry on with the conversion!
Wayne
Quicky