1) I would almost always just open with the person's name or callsign. (Jeff, are you there?). In some situations a speaker might begin with 'calling'.
2) That is fine. I would consider dropping the 'some', and just saying "I need to catch up on sleep", or "I need to catch up on my sleep".
3) That is fine. "Pleasant" is another words that's used quite often when describing someone's dreams in the past tense.
4) Yes, although not without answering the question first. "I'm good, how are you?", or "Fine, how are you?" are common. Also common is, for example: "I'm good, and you?".