Does Walmart have the characteristics of a firm in pure competition?

Wal-Mart is almost certainly not an example of pure competition. Pure competition is characterized by a very large number of sellers - each with an almost infinitesimally small market share - selling a non-differentiated product. Wal-Mart's market share is immense (as you stated) and they differentiate their product through branding measures that include everyday low prices, convenient hours, etc. There can be tough competition in every market structure (except monopoly) but that does not mean that the market meets the definition of pure competition.