Recall if $ f\in L^1_{loc}, $ the result for #3 a follows from Lebesgue differentiation theorem.
Next if $ f\notin L^1_{loc} $ consider the following: WLOG $ f\geq 0 $ by replacing $ f $ with $ |f|. $ Let $ x\in \mathbb{R}^n $.
Case 1, $ \exists K\subset \mathbb{R}^n, K $ compact, and$ \int_kf=\infty $
