Funding during graduate study (phd, masters) in math in the US

I have some questions and concerns in mind:

1) When somebody says a program is "funded", does that mean the money is conditional (whether or not he TAs or not) or unconditional? Or is it clarified in context?

2) Is there such a thing as entirely unconditional funding? If it's not tied to teaching, will it always be tied with progress (or something else)?

3) Are there programs that will ask you to take out loans? In other words, do (most) schools generally have some sort of funding available? How does this depend on rankings/tier? Is there a specific ranking, say 50, below which you'll mostly likely need money through loans?

My personal concern is whether or not I can depend on being funded, even if I'm not a very strong student.