Reviews take anywhere from 10 minutes [very rare but possible] to a couple of years [and maybe more]. Depends on too many factors to predict.
Updates for listed sites are done by going to the category where the site is located, and pressing the Update URL link in the top right. You will then be asked for the URL and the changes. Since the request can be done by anyone [not just the site ownere], any suggested changes must be verified and matched against the contents of the site.
Changes in the listing to reflect an incorrect listing, or the fact that the web site has changed, or a request that it be moved to a different category [where appropriate] would be welcome.
Suggested changes that do not match the guidelines e.g. trying to get keywords stuffed into the description or adding marketing hype would be ignored.