A “hardline” phone is a phone that connects to another network by means of an artificial wire. Even if it is a “cordless phone”, because the base set connects to the phone grid via a physical wire, it can still be called a “hard-line” computer.

Both are really okay; usage depends on the audience you’re writing for, and then your personal style/personal taste, in that order.

Can I make short sentences hyphenated? What should I do? Generally, in formal, professional writing, the decision to hyphenate or not will be made by the editorial staff for which one is writing. The reasons why it is so, are unclear. Toward the academic level, however, this decision will be made either by the professor, or — if not — devolve to the author himself/herself, as to his/her particular interest and the manner in which they relate to the matter.

What is online? In speech I tend to use one, depending on context and rhetorical aim. For example, I generally hyphenate when the word is used as a predicate complement (“I am on-line”, “I need to get on-line”), and not when it’s just a straight adjective (“It’s an online game”, “Online accounts are down right now”). They aren’t hard and fast, even for me; if I’m writing for younger audiences, I will tend to just go with it: “online”, because that seems to be how things are trending with their age group.