We present a newly implemented single-pulse pipeline for the PALFA survey to efficiently identify single radio pulses from pulsars, Rotating Radio Transients (RRATs) and Fast Radio Bursts (FRBs). We have conducted a sensitivity analysis of this new pipeline in which multiple single pulses with a wide range of parameters were injected into PALFA data sets and run through the pipeline. Based on the recovered pulses, we find that for pulse widths $rm < 5 ms$ the sensitivity of the PALFA pipeline is at most a factor of $rm sim 2$ less sensitive to single pulses than our theoretical predictions. For pulse widths $rm > 10 ms$, as the $rm DM$ decreases, the degradation in sensitivity gets worse and can increase up to a factor of $rm sim 4.5$. Using this pipeline, we have thus far discovered 7 pulsars and 2 RRATs and identified 3 candidate RRATs and 1 candidate FRB. The confirmed pulsars and RRATs have DMs ranging from 133 to 386 pc cm$^{-3}$ and flux densities ranging from 20 to 160 mJy. The pulsar periods range from 0.4 to 2.1 s. We report on candidate FRB 141113, which we argue is likely astrophysical and extragalactic, having $rm DM simeq 400 pc~cm^{-3}$, which represents an excess over the Galactic maximum along this line of sight of $rm sim$ 100 - 200 pc cm$^{-3}$. We consider implications for the FRB population and show via simulations that if FRB 141113 is real and extragalactic, the slope $alpha$ of the distribution of integral source counts as a function of flux density ($N (>S) propto S^{-alpha}$) is $1.4 pm 0.5$ (95% confidence range). However this conclusion is dependent on several assumptions that require verification.
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