To "live down" means to live long enough so that an embarrassing moment is no longer remembered. You usually hear this in terms of someone "living down" something they did that everyone keeps making fun of them for. Another way to say that would be to say "I'll never live that down!" when you do something embarrassing.
To do work and focus
Distill down, or boil down, as an idiom, means to get to the essence of something, or to simplify it.
I've never heard that idiom before. Perhaps you mean DOWN AND OUT, which means that the person is at a low point in their life, that they're poor in every way and not likely to make a success at anything in the near future.
sit down come over to
This is an idiom meaning to narrow your focus down. It can also mean to narrow your aim and focus on one thing to hit. Picture the zero as a target and you get the idea of the idiom.
This is not an idiom. They mean that someone literally has a tapeworm inside their intestines. It's a parasitic organism.
It means you are looking to move, to live somewhere else.
i don't now
This isn't an idiom because it means exactly what it seems to mean. It's a saying - you can't live tomorrow yet, so today is more valuable.
If someone "jumps down your throat" it means they react very angrily about something you said.
The idiom down to the wire means to the very last possible moment. Therefore, the entire phrase would stand to mean that "it went to the very last split second and we almost missed your flight, but made it."
This is not an idiom. The verb "lay" is the past tense of "lie," and means that whatever or whoever the subject of the sentence may be, they were laying down on top of some hay.