Hey there, "Take literally" is used when you might be ignoring the context of what the person is saying a little, for example if I said "I've had such a stressful day, I just want to jump off a bridge" and you said that you took what I said literally, you'd be saying you thought I was really going to jump off a bridge. "Take at face value" is like saying that you will take however something seems as how it is, for example if you've watched a trailer for a movie and you thought it looked bad and then assumed the movie is bad, that is an opinion you have taken at face value. In this example you can't really say that your opinion is something you've taken literally which I hope clears up that they aren't necessarily interchangeable.

Do not worry too much about this. Very few people use the words 'at face value'.

In your sentences for "literally" In the first sentence you are stating that your actions seriously. "I take everything seriously." In the second sentences you are stating that whoever is talking you are really believing what that person said. Boy: I love you, Mary. Mary: I will take your word for it. ( This means literally to believe). The "face value" comment is an expression or idiom to say that there is nothing more than meets the eye and digging deeper isn't likely to reveal anything interesting.