Spindle assembly.
Spindle housing.
Spindle shaft, or even just shaft.
And the pulley. Also called a sheave i think it is. Grumpy will know.
Do you have a fair to good assortment of tools??? Well actually you only need a few basic spanners and sockets.
I would assume the blades are the same length on both sides.
Remove the blade off the busted spindle. Fit that blade to the good spindle. Spin it by hand, use a magnetic something off the fridge or just the edge of the deck or something to give you a refference point and watch closely. You need to make sure that the blade is still spinning flat. If it is it is good to use again, if not you will need a new one.
The spindle housing is busted. Undo the 4 bolts. Remove the assembly from the deck.
Take your assortment of bits into the dealer and tell them you want another under warranty and a new belt as well and the blade if that is no good.
Two months to fix something under warranty, that is just plain rude.
By the look of it your only issue with DIY will be doing up the blade snf pulley bolts.