Hi Andy,
the widening of the tip is indeed for armour piercing. As to repairing the heavily rusted areas.....I would leave it alone. Metal 'fillers' do not have a metallic look and would be very noticeable. Infilling with welding would be possible, but heat 'build up' could affect the blades temper. So it would have to be done a little at a time, ( very labourious) to allow it to cool between welds. Obviously the finished weld would have to be ground down to match the profile of the blade and probably would still show up as there may be colour variation between the 'weld' steel and the blade.
Unfortunately the rust damage considerably de-values it.
If you are unhappy with the Katar, and want to sell it you could always PM me
I actually like old 'beaten up' warriors
Kind Regards David