How do you interpret the good-night saying of "Sweet Dreams"?

It can be interpreted so many different ways, but don't stress over it. If someone says it to you, it means that they want you to sleep well, maybe even think of them. Just know that they are thinking of you, and just want you to get a good nights rest.

It can be just a casual parting remark, something that one says out of habit, especially if the family says it a lot. I wouldn't read too much into one parting remark. It might be as meaningful as "Good night. Sleep tight. Don't let the bed bugs bite."

Be careful not to fall into the trap of trying to analyze every single phrase and word a person uses. Relax and figure things out by overall behavior and full conversations over time.

It basically means have a restful night sleep.

Having a Sweet Dream as opposed to having a Nightmare.

I would not read anything romantic into it

It is a very caring way of saying, I want you to refresh your mind while you sleep with happy thoughts.