The answers above give some great examples for how and what to test regarding web apps.
I'm going to respond real quick to a few other points in your question:
When I interview for positions on our QA team, I have two primary concerns: the way the interviewee thinks and their knowledge of the underlying technology domain.
I've interviewed students and professionals whose idea of testing an application is to "turn it on and see if it smokes." They often had a great understanding of the product technology (e.g. the innermost workings of HTTP), but they couldn't connect this knowledge to a practical and systematic application (e.g. how to test a database app which communicates with a server via HTTP).
I've also been deluged with test cases by interviewees who simply didn't understand the underlying technology being exercised (e.g. networking tools, simple Java apps, database clients). Their lack of understanding greatly impaired their ability to arrive at insightful and useful test cases, even though they were able to provide a large number of tests.
In either case, I would highly recommend (for any type of interview) you first research the field in which you would be working prior to the interview. Don't just attempt to integrate jargon and buzz words (you'll look foolish if you get them wrong), but investigate the position with an intent at learning what it entails. The more you know prior to the interview, the better you'll understand the context in which the questions are coming from.
Also, never hesitate to ask for clarity on an interview question. I get annoyed when someone doesn't understand what I'm asking and tries to fake it. If someone asks me to reword or clarify something I've said, I usually take this as a good sign of someone who desires to communicate accurately.