I am wondering if we must use both of the bold parts together? Isn't one of them ellipsis? Must we always use both pairs - bold parts together?
I want to settle down, and start a family.
I want to get married and settle down.
Not at all. They're commonly used together, because when they are used together they evoke the full meaning of "in the traditional way." A person could settle down without starting a family or getting married by simply buying a house and deciding to live there for a long time. Or, you could get married and the both of you could go exploring and adventuring for a while, or even just live a kinda drifting lifestyle indefinitely, even while starting a family.
Using both of them together evokes a lot more, though, buying a house, starting a career, getting married with kids and maybe a pet or two, the way you're culturally "supposed to", and so it makes the family members who hear it happy and calm, like everything is going right. Using just one would inevitably provoke a nervous question about the other.
