Cocoa liquor is when the cocoa beans are ground into a paste. The term "cocoa liquor" is used to describe finely ground cocoa beans. During grinding, the mill gets hot and the ground cocoa beans...
No, cocoa mix can be used either as a cooking ingredient or as a mix (like for chocolate milk) but baking cocoa is strictly for baking, for things like cookies or cakes.
"The density of the cocoa liquor was reported as 1110 kg/m3 at 100 °C"
found in:
Modelling and experimental evaluation of high-pressure expression of cocoa nibs
by M.J. Venter, N.J.M. Kuipers...