On this age machine''' you probably should replace the thermal paste'''. BTW that's an advanced DIY so you might need some help. That a fan is constantly running full blast means ''something is overheating and the "default fix" is to run the corresponding fan at MAX to reduce chance of component damage from over heating.'' It could be your CPU or the GPU that is overheating. Running AHT should report which component is hot. A fan app might also catch this.
As to the black screen hang/no reboot. ''If you have peripherals attached - ''try putting them away ''(eject mounted volumes) and powering off or unplugging them before shutting down''. You might have a failing/misbehaving peripheral.
''If this Answer is helpful''' please remember to return and mark it''' Accepted. ''