You can get away without using the bleed screw. Try loosening it gently by hand. If it doesn have it, leave it. Just leave the cap off for a good while and let it burp itself. Pour in the coolant slowly.
I have had my 8th gen alternator fail.
Its not that hard of a job to do to be honest. I did it myself on the driveway. I think I took the cooling fan out to get more room.
I have had this exact same problem.
There are two types of hub.
https://www.amazon.co.uk/dp/B071VQYWLR/ref=au_as_r_pf_gs?_encoding=UTF8&selectVehicleSource=garage%20select&submodelId=29482
This one above will fit...