Wiktionary gives the meaning "you" for the character 妳 (nǐ), and tā (either 他 or 她).
Is there a formal / informal difference? Which should I prefer in general usage?
妳 is in theory a feminine form of 你, but it's rare because not many people care about the supposed masculinity of the 亻element. 他 and 她 are 'he' and 'she' respectively, as any reasonable dictionary will tell you. There is a formal/informal distinction for 'you', but it's 你(normal) and 您(formal).
Whatever your sources are for the reading 'hai' and the meaning 'you' for 他, you should ditch 'em, they're unreliable.