The difference between the first two sentences is unambiguous:
(a) She has only ten dollars means that she doesn't have any more money than $10.
(b) Only she has ten dollars means no one except her has ten dollars.
Thus (a) when only is placed between the verb and the object, the object ($10) is characterized as not enough; (b) when only is placed before the subject the action of state is limited to the subject, not anyone/anything else.
The difference between the other two sentences is ambiguous because meaning (a) above
can be shown with only placed before the verb, in which case your two sentences have the same meaning - Meaning (a): I answered 4 questions, which wasn't sufficient.
(c) when only is placed before the verb, it can mean that the action/state of the verb, and no other action/state, happened or existed.
Thus, I only answered four questions could mean:
Meaning (a): I answered 4 questions, and this action/quantity wasn't sufficient.
Meaning (c): I answered 4 questions; I did not (for some strange examples) ask them or sing them or...
In most, but not all cases, the context would resolve such ambiguity; presumably, meaning (a) would be obvious for your context.