Okay. To keep one's head - it can be positive as well, but more often, it's negative with this one.

它也可以有积极的含义，但是更常见的是负面的含义。

Next, to keep one's head above water. If you go under, then you're not surviving.

接下来，使自己免于负债。如果你破产了，你就无法存活了。