a) is in the past tense. It refers to the past - ie. to the time she started to work. The implication is that she will have had little to eat after she started working, but that's still in the past.
In "With little to eat, she starts to work", this refers to the present. Again, the implication is that she will have little to eat in the future (all other things being equal, which they might not necessarily be). But you can't even say that sentence refers to the future. It refers only to the present. "She has little to eat" is present tense. She might die without food, but that is a supposition. The sentence itself is not a reference to the future.
2) No, "with little to eat" doesn't refer to any time period by itself.
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