Usability testing is a method in which developers are able to get feedback on the operation/usability of the product they are designing. In particular, usability testing for websites allows for the developer to ensure that everything on the site not only works as intended but draws interest from the person browsing the site.
Anyone can really be a usability tester all depending on what the site owners are looking for, however, there are many people who are trained tester that will looks for flaws within the site.
The site owner or an appointed evaluator will give a list of tasks that someone who would use the site on a day to day basis might try. For in person testing, it is easy for the evaluator to actively see where the tester’s eyes are drawn to first, where they start looking for certain links/tabs, and how long it takes them to complete the activity. For remote testing, and evaluator may have software that are able to track certain stats about how the tester went about completing the tasks by tracking clicks, eye movements, and time taken to complete tasks.
To learn more about site usability testing check out usability geeks article An Introduction to Website Usability Testing
Yes, browser validation is an incredibly important part of any website/web application life cycle. Ensuring that the project runs smoothly if at all on as many browsers as possible ensures that the product is accessible to everyone.
The short of it is that multiple browsers, or at least the most popular ones, have your site tested against them. During this testing a myriad of tests are done to ensure the sites usability on all the browsers such as accessibility testing, smartphone and tablet testing, login form compatibility. Those are just some of the many tests done on each of these browsers.
To learn more about browser testing check out pcloudy.com’s post titled How does Cross Browser testing improve the User Experience?