Is it the year a PDGA member first plays open or the year a player first takes cash (i.e., gives up amateur status)?

What are the benefits of being a rookie, besides eligibility for rookie of the year?

It's the first year you renew as a Pro. If you accept cash in the previous year, it depends on when you accepted cash. If you accept cash before Am Worlds, then that's your roookie year and you can't play in Am Worlds. If you accept cash after Am Worlds, then the following year is your rookie year. No benefits for rookies other than potential for Rookie of the Year award (and now you usually play for cash.)