Is there a relationship between acidity of the water solution and oxidation/reduction reactions?
Fenton chemistry based on iron is definitely more reactive at lower $\mathrm{pH}$. This is due, in part, to speciation issues and associated solubility. Source: 'Effect of $\mathrm{pH}$ on Fenton and Fenton-like oxidation', by 
Jung YS, et al., at https://www.ncbi.nlm.nih.gov/pubmed/19278159.

However, the use of chelates (like EDTA) can expand the $\mathrm{pH}$ range of reactivity (see full paper at https://www.jstage.jst.go.jp/article/jwet/11/1/11_21/_pdf ).

There are other transition metals, like Copper, which appear to be active in a much wider $\mathrm{pH}$ range where the chemistry is referred to as Fenton-type. There is an old french patent on water purification (from microbes,...) based on copper ions ($\ce{CuSO4}$ in small amounts) and natural waters containing dissolved oxygen. Interestingly, the addition of EDTA is still recommended, but now as a means to TERMINATE the redox reaction at near-neutral $\mathrm{pH}$.

There is a similar property for Cobalt ions, however, its toxicity has generally precluded it from commercial applications (like remediation of polluted waters through advanced oxidation processes referred to as AOP). Here is a reference on non-iron fenton processes at https://www.sciencedirect.com/science/article/abs/pii/S0304389414003239 and a more general review here, click on pdf download feature at https://www.researchgate.net/publication/322020986_A_Review_on_Advanced_Oxidation_Processes_for_Effective_Water_Treatment/link/5a4b0cd5458515f6b05b5221/download).