1) "It´s always been dead" - is grammatically correct and natural. Whether it’s true that it’s always been dead and what exactly dead means in this context, I don’t know.
2) I would say “facial expression” or “the expression on her face”. “Face expression” may be correct, but I haven’t encountered it myself.
"I inferred from her facial expression that she doesn’t enjoy working here" could be correct , but it could also be using tenses incorrectly. Your question can only be answered
with certainty if you provide enough context to make the exact sequence of events clear.