1. According to Julius Schwartz, Hal Jordan was intended to look like what famous actor?
In a letter column from Green Lantern #3, Julius Schwarz revealed that Hal Jordan was supposed to look like Paul Newman.
2. True or False: Hal Jordan did not know of the existence of the Guardians for several years after his debut.
False, but it's close. The Guardians were introduced in GL #1, but they did not encounter Hal or GL in the story, but rather they beamed an "energy twin" of him to Oa as discussed here:
As a result, Green Lantern apparently didn't know about the Guardians until Green Lantern #7:
Which was about 20 months (or less than two years) after Green Lantern's debut.
3. Who was Green Lantern's love interest in the far distant future?
Iona Vane was Green Lantern's girlfriend in 5700 AD.
4. What villain was initially a competitor with Green Lantern for the affections of Carol Ferris?
Hector Hammond, as Carol ruefully remembers here:
A "flighty" mind indeed.
5. What Green Lantern villain's motivation for committing crimes was to bring power and fame to his native land?
Sonar, one of the weirdest DC crooks of all time, as I discussed here.
I'm going to give everybody credit for #2, because I screwed up and didn't check the question myself, assuming that I knew the answer, and 20 months versus "several years" is too close. Jim gets 1, 2 and 5 right. David Morefield rings the bell with all five right, and Michael Rebain gets 2,3 and 5.