Right, I like to say there are "से verbs" (like उससे बोलो) and "को verbs" (like उसको (or उसे) खाओ.) Most of the time you will see को verbs being used, but occasionally, से verbs are used, से बोलना, से बात करना, से कहना, से प्यार करना, से नफ़रत करना, etc. You just gotta get used to it I guess.
By the verb that comes after! Not sure what you mean by neutral, like someone who is gender neutral? I haven't actually encountered that in Hindi thus far, so not sure how it works. But if you had, say, just a male and a female, you could say जब मीनु राजेश (को) देखती है (When Meenu sees Rajesh,) the sentence can end in two different ways, you could say वह उसको खाना देता है (He gives (him/her) food) or वह उसको खाना देती है (She gives (him/her) food.) Conjugation of the verb depends on the gender of the person doing it, so you can just work it out from there, who the person they're giving food to is. It's easy in this situation, but with a situation with multiple males and multiple females, it wouldn't just make sense to say simply usse or usko, same as in English, "him" doesn't mean much in a group of multiple males, so at that point people would be referred to by name :).