The names all have three A's as their only vowels. This goes with Antonio STARABBA.
The letters in the last name can be formed only with straight lines, matching Gene KELLY.
The third letter in the last name comes alphabetically after the second letter (rABin, aSTaire, etc.), matching Franco ZEFFERELLI.
Notes: I only got part 1 during the test, which took me no time. (To be honest, it was my father who noted the part about the three A's; I thought it was unusual enough that they all had only A's as vowels.) I spent several minutes on Part 2 during the test, but didn't solve it until a quick glance right after the test. D'oh! Part 3 took me about five minutes after the test as well, I barely looked at it during the test..