2004 impala 3.4 water pump replacement

i seem to be having a leak from around the pully. coolant sprays out sporatically in very small amounts(drops). this pump was replaced by a shop in the last 5 years.

1. is it possible this is just a gasket and not the pump itself? how would i tell?

2. attached is a video of what the temp guage is doing. i was advised my thermostat sticking shut (changed in the last 5 years). i did notice some grey sludge in my radiator upon refill after finding the leak. wondering if this is a product of air, or the sludge?

https://www.youtube.com/watch?v=fW8h6ZN5MJQ

There may be an air bubble in the system. This would account for the lack of heat from the HVAC system and the wild fluctuation of the gauge. It would also explain the sludge creation in a DexCool system.

If there is a leak from the pump or the gasket, the pump would need to be removed to repair the leak. It would make sense to install a new or reman pump at that time just to avoid the possibilities of a shaft seal leak, slipping pump impeller, or failing bearing. The replacement pump cost is negligible.