1. What is your current and expected salary? It's a quick filter, in two ways. If an applicant is making well above what we offer, I know that we shouldn't move forward with them. People almost never go backward on salary, and when they do, they rarely work out in the long term. It tells me how senior they are. For example, a software developer making $100k and one making $150k are fundamentally different candidates. It tells me how I should interview them. A candidate at $100k would fail the $150k candidate interview, and the $100k candidate interview would be too easy for the $150k candidate. I get some important data. If, after interviewing several candidates for a position, I find that all of them are making more than what we're offering, I know we need to rethink our offer.

Email the professor, have a conversation. Then they will usually ask about your relevant classes and determine if you are a good fit. Usually strong interest will get the job.