Rademacher complexity beyond the agnostic setting
(a) If you don't assume that you're "competing" against $f\in F$, you must make some assumption about the larger function class to which $f$ belongs -- otherwise, by standard no-free-lunch theorems, you will not be able to give any meaningful risk decay rates (which is what Rademacher complexities enable you to do). Alternatively, you could assume something about the distribution (trivial case: it has finite support). Then you can get distribution-dependent rates.

(b) For unbounded losses, you typically need additional assumptions such as convexity or tail decay. See, eg,
https://papers.nips.cc/paper/3894-smoothness-low-noise-and-fast-rates
and
http://proceedings.mlr.press/v32/kontorovicha14.html

(c) It looks like you're looking for a lower bound on the risk in terms of Rademacher complexity. Any such result would have to be distribution-dependent. Since Rademacher complexity is majorized by covering numbers (via Dudley's integral) and also minorized by these (Sudakov inequality), you could probably use the covering-number characterization of learnability:
https://www.sciencedirect.com/science/article/pii/030439759190026X