1. What famed superhero was the first to be declined entry to the Legion?
Superboy was declined admission in the very first Legion story. However, it turned out to be his final test to see whether he was worth of induction, and he passed with flying colors. George C, Michael Grabois and Kryp44 all answered correctly.
2. What famed superhero was the first to really be declined entry to the Legion (temporarily)?
Supergirl was declined admission into the Legion the first time she joined, ironically because red kryptonite had changed her into an adult, and the Legion (at the time) only allowed teenagers to join. George C, Michael Grabois and Kryp44 all answered correctly.
3. What superhero was the first to decline an offer by the Legion to join them?
In Adventure Comics #315 (December 1963) Stone Boy was selected by the Legion as the most worthy member of the Legion of Substitute Heroes (a Legion backup) to graduate to the big club. But in a classic display of loyalty, he decided to remain with the Substitutes. George C, and Michael Grabois got this correct. Kryp44 did mention the third member not to join the Legion.
4. What later superhero was thought by Mon-El (who had a senior moment) to be the first to decline an offer by the Legion to join them?
In Adventure Comics #320 (May 1964) Dev-Em, a former Kryptonian juvenile delinquent who has reformed, declines membership in the Legion:
In fairness to Mon-El, he was not present in the issue where Stone Boy had declined entry. But one would expect that he would have heard about it later. Michael Grabois and Kryp44 both answered correctly.
5. Who was the first Legion member to "die"? Who was the first Legion member to really "die" (for good)?
I put "die" in quotation marks there to give a little hint that there was something of a trick in the answer. Lightning Lad "died" in Adventure #304:
But he was brought back to life by the sacrifice of the original Proty. This was a surprising story, because although villains had often "died" at the end of one story only to be resurrected at the beginning of their next appearance (the Joker and Dr Doom quite noticeably), this was the first time that a hero had "died" for several issues and then been brought back. It would not be the last. George C, Michael Grabois and Kryp44 all had the right answer.
The first Legion of Superheroes member to really "die" was one of the three bodies of Triplicate Girl, as shown on this memorable cover of Adventure Comics #340:
Fortunately, she had already split into three persons before this execution, and so she became renamed Duo Damsel.
Kudos to Michael Rebain for coming up with the trick answer here. Of course, Ferro Lad is the first Legion member to die, die, die, with no resurrection and two other bodies left over