- 1) In what ways does the 'Great Hakurei Barrier' effectively prevent the Lunariens from entering exactly?
To start off, it doesn't actually specify "Great Hakurei Barrier" in the original text, it just says that Gensokyo is a closed space. This seems to be added in translation (IN-era translations, oh boy), but it is indeed stated to be specifically the Barrier preventing them from entering in the Border Team ending.
Almost a hundred years after Gensokyo was sealed (i.e. before 1985), Reisen entered Gensokyo, but she didn't come straight from the Lunar Capital like Rei'sen had. She had fled before the Lunar "War", which started in 1969. This is corroborated by Toyohime mentioning she left "over 40 years ago" in CiLR (2009). Eirin also mentions a few chapters earlier that Reisen showed up "around 30 years ago". The ambiguous time gap between 1969 and 1979 suggests that she spent time in the outside world, then (as IN profiles word it) heard rumors of Gensokyo and entered it "somehow". That being said, CiLR also says she used a Lunar Veil. The difference is that Rei'sen came directly to and fro, whereas Reisen would have taken the veil to Earth, but not entered Gensokyo until later.
In IN, Eientei was built in Gensokyo long before it was sealed away. After Eirin met up with Kaguya, the emissaries slowly stopped coming. (Later in CiLR, this is explained by the Watatsuki sisters taking over and not caring about trying to get Eirin back, and then everyone else losing interest.) Once Gensokyo was sealed, the logic of "the emissaries couldn't get in even if they wanted to" is consistent, since Reisen would not have come directly into Gensokyo, but came from the Outside. So as far as IN is concerned, any emissaries couldn't get in.
As of SSiB/CiLR and on, the understanding is that going directly between Gensokyo and the Far Side of the Moon is simple because the barriers between Gensokyo and the Outside, and the Far Side and the Near Side, are similar. This is how Toyohime travels in SSiB and Inaba, it's how Rei'sen traveled, and it's how the Vampire party got to the Moon. Since in CiLR the time difference between Reisen escaping the Moon and arriving in Gensokyo is still present, I don't think that the detail of Reisen coming from the Outside was retconned. But obviously, the claim that emissaries couldn't enter Gensokyo is now retconned in a rather big way. The fact that a Lunar Veil coming down from the Moon in CiLR isn't seen as impossible by Eirin, who would have been previously told that it was impossible, further supports this being retconned.
In the ongoing canon this retcon isn't a problem at all, since the Watatsukis don't care to take Eirin, Kaguya and Reisen back, and no emissaries were ever sent. Eirin's fears were still unwarranted because while emissaries
could enter Gensokyo, there hasn't been any
trying for centuries. The moon rabbits saying they were coming to take Reisen back, as well as the claim that they were going to war again, was a lie in both canons.
the moon saga is complicated as fuck
- 2) Did Eirin successfully manage to carry her plan of sealing the passage b/w the Moon and Earth before she was defeated? If so, why is it that even regular moon rabbit can enter Gensokyo? If not, just say NO.
The reason I'm asking this is that I read somewhere in this particular forum that she indeed manage to successfully manage to carry her plan...
She did. You might have heard me say it because I'm pretty sure I've posted about this a number of times.
Eirin's plan was to seal away the full moon, on the night of the full moon. The boundary between the Moon and the Earth exists only at that time, so she just had to replace the moon for one night. She says as much in the dialogues that she would return the moon once day broke. Eirin's plan already succeeded, which is the whole premise of the incident. On the protag side, they just saw that the moon was fake and this was a problem, so they froze the night in order to find the perpetrators. Reimu asserts that they need to return the moon before the night ends. Since Eirin's plan was to return the moon after the night ended, Eirin had to keep the moon sealed. Even once the protags arrive at Eientei, neither side realizes this predicament. Eirin and Kaguya decide to just play with the protags until the night ends, but it never will, and so everything up to this point is just a rather comical standstill until Kaguya realizes the problem and fast-forwards the night.
Kaizaki would be incorrect here; it isn't as though Eirin was actually keeping anything out to begin with, and Eirin had planned to take down the fake once the night was over, so ending her technique didn't really do anything.