power steering pump replacement

Were these symptoms the reason for the pump replacement in the first place? If not, what was?

It almost sounds like you've got a blocked return line and system pressure is going through the roof, resulting in the pump heating and spitting fluid and the brakes being forced on.

I'd exercise extreme caution: If a hose burst due to over-pressure, it (or parts of it) could become ballistic and do serious damage or injury in addition to spraying hot fluid at crazy velocity. Consider taking it all down inspecting everything for blockages before running it again.