Can the word “Greetings!” be just sent in a message by itself and what could the meaning be?
Yes. The meaning is pretty universal. It means “Hi, I’m thinking about you”. And if it coincides with a special event, the recipient presumes it is matched to that event. In fact, Christmas cards often have “Seasons Greetings” printed on them. I know someone who annoyingly used to say “Greetings” instead of “Hello”.