I'm living in a Cantonese speaking area (Hong Kong) and my Mandarin teacher (from Taiwan) claims that the multiple written forms of the third-person singular pronoun were introduced a generation or two ago in order to be able to more faithfully translate foreign works into Chinese. She says that many people, particularly the older generation, always use the older character, the one that now means "he".

As far as dialects that might have different tones to distinguish he/she/it, it's possible. It's also possible for a dialect of Chinese to have wildly different pronunciation of those characters, maybe something like "ta" , "ki", "zu".

Chinese dialects differ by more than most foreigners expect. It goes far beyond "Texan arguing with a Brooklyn cabbie" or "Texan arguing with an Aussie" level of dialectal differences. Cantonese and Mandarin are less similar than Italian and Portuguese. Cantonese uses the same two characters for rooster as Mandarin uses (公雞 "gong ji"), but reverses the order (雞公 "gai kung"). "gong" and "kung" sound pretty similar, but "ji" and "gai" are totally different. (On a side note, the Thai word for chicken is also "gai".) Also, I need to be careful about mixing up the numbers between Cantonese and Mandarin... the Mandarin word for one differs only in tone from Cantonese word for two, and my Cantonese tones are terrible. (1 2 3 4 5 is "yi er san si wu" vs. "yat yi san sei ng".) I have a friend who (I have no idea why he was so crazily naive) is a native Cantonese speaker and thought he could just go to Shanghai and speak Cantonese with a Mandarin accent and be understood. He ended up speaking English his whole time there because Cantonese just sounded like gibberish to the Shanghainese and Mandarin speakers.

Gender distinctions in the Standard Chinese written forms 他 (he), 她 (she), 它 (it) are indeed a recent introduction. In Cantonese there's a single character for he, she, or it (佢, pronounced keúih). This is a different word entirely from Mandarin tā, not a different pronunciation of the same word like 雞 being pronounced jī in Mandarin or gāi in Cantonese.

Because, as you pointed out, there's no mutual intelligibility, Cantonese and Mandarin are considered by linguists to be separate languages.