Gerd Gigerenzer is widely acknowledged as one of the world experts in the cognitive aspects of numeracy or, alternatively, innumeracy. He has many papers and books on these topics referenced on his website (https://www.mpib-berlin.mpg.de/en/staff/gerd-gigerenzer). One of his key texts is his 2002 book Calculated risks: How to know when numbers deceive you. Read the abstract here: https://www.mpib-berlin.mpg.de/en/research/adaptive-behavior-and-cognition/publications/books/calculated-risks
Related to Gigerenzer's work is cognition-based decision theoretic work that looks at the way information is presented. A representative paper here is Dan Goldstein's The Illusion of Wealth and its Reversal available here ... http://rady.ucsd.edu/docs/seminars/goldstein.pdf Here's from the intro:
Recently, researchers and policy makers have started to pay more
attention not just to choice architecture but also to information
architecture: the format in which information is presented to people.
Research in information architecture has shown, for example, that the
caloric content of food can be well appreciated in terms of the amount
of exercise it would take to work calories off, and the comprehension
of cars’ energy efficiency can be enhanced by presenting information
in terms of gallons per 100 miles instead of miles per gallon. This
paper investigates information architecture, though instead of
consuming calories or gasoline, we address economic consumption in
An important recent addition to the literature is Berkeley Dietvorst's research into "algorithm aversion" and decision-making. Dietvorst contends that wrt predictive modeling, the technically naive and/or illiterate tend to assume that predictive models are a "magic bullet" or perfectly informative and when the algorithms prove to be, at best, weakly predictive, then the typical response is to reject quantitative solutions altogether.
Then there are bloggers like Kaiser Fung who maintains his Junkcharts website critiquing the graphs and visualizations of major pubs such as the NYTs or the WSJ
Related to your question of visualization is the work of design experts such as Manuel Lima who maintains a website VisualComplexity.com covering the many approaches to this. Lima also teaches data visualization at Parsons School of Design in NYC.
Besides Parsons, other design and visualization institutions include:
College of Design and Social Context
UCLA's Culture Analytics Institute
Google's Cultural Institute
A MoMA design exhibition and book
In terms of conferences there is the Eyeo Festival
In R software, the visualization guru is Hadley Wickham
In SAS software, there is Rob Allison
Finally, there are no shortage of "one-off" kinds of websites:
http://infosthetics.com/ great visuals of govt data
How to display data badly by Karl Broman
Maria Popova's Design and Communication blog
Gallery of Data Visualization
Periodic Table of Data Visualization
Our World in Data
This just begins to scratch the surface of what's out there...