Fallout 2:Entering the Vault

[Lopov]

Ok I got into the Vault City with false papers and then talked to Lynette.I made her angry but she didn't kick me out of the town, I can still communicate with her but she doesn't give me the Gecko Power Plant quest as it is supposed to be.I also can't pass Gregory's citizenship test.So - is there a way to still get a citizenship?

The quests I can do now are only those from Sergeant Stark (scouting around Gecko and travelling to NCR) and none other.

If I do Gecko PP quest although Lynette didn't give it to me, is there still a chance to become a citizen?

And final question - if I screwed it totally with angering Lynette is there still an option for finishing a game without entering the Vault at all?

[Amorphium]

there is another npc who gives you the task to repair gekkos powerplant and will grant you citizenship regardless of what lynette wants, hes in the same buildung, in the left room.
IIRC you dont need anything from vault city to finish the game, although the ending might be different and you dont get combat armor implants/cant donate sperm

[Kipi]

IIRC you dont need anything from vault city to finish the game, although the ending might be different and you dont get combat armor implants/cant donate sperm

Spoilers below, highlight to read

Spoiler

From the Vault itself you get location of Vault 15, from where you can get the location of Vault 13

End of spoiler