Surely 'is me servat et ego eum servo' would make more sense? Using ille as a personal pronoun was a later innovation.
Not "They save me and I save them"? If I were trying to talk about a person of unknown or unimportant gender, which latin pronouns should I use?
Last time I checked, Latin has no gender-neutral pronoun (or something like that). That idea doesn't exist in Latin. You must assume the gender of people you are referring to all the time. Some schools suggest the use of masculine words like ille or is for a group of mixed gender, following the logic of current Romance languages. But also, it's just a suggestion. Some also suggest to paraphrase the sentence in different way like passive structure to omit using pronoun at all.
Latin does indeed have neuter pronouns. Suum is the nominative neuter of the reflexive, and Id is the nominative neuter of the direct, which you mentioned. (Is is the masculine of Id) Pronouns don't have to refer to people, and the pronoun has to agree in gender, number, and case with the thing that it refers to. You could be talking about a monster, or maybe even an inanimate thing like silver. So "argentium suum" would be "the silver itself"
The original question by Jacob is about Latin equivalence to English gender-neutral pronoun "they" (sometimes called singular they).
I think you misunderstand the meaning of gender-neutral personal pronoun which is semantical and NOT always the same as grammatical neuter gender pronoun. Gender-neutral here is for human and it means "covering both male and female gender (of human)".
I don't think neuter pronoun id or illud should be used to refer to person as it serves the meaning of a thing not a person. Using id to refer to person seems very dehumanizing and inappropriate as the word itself is not ment to refer to person but rather 'that thing' or 'this thing'. Same analogy as the difference between quid (neuter = thing) and quis (mas/fem = person). Like you don't use it to refer to a person in English.
Ille is masculine. Your question about unknown gender is a heavily debated one in Latin speaking circles.
Ille is a demonstrative masculine pronoun meaning "that". Given that it is masculine, we have to infer that it refers to a masculine person. In Latin masculine is the collective gender (And generally in Latin literature most active agents are men anyway), so when in doubt I would use that personally.
"They save me and I save them" -> Illi/ii me servant et ego illos/eos servo.
The verb servare means to save. It gives us such words as conservation, preservation, to preserve, to conserve. You're thinking of servire, which means to serve. It's a completely different word. :)
Double check on William Whitaker's Words to make sure: http://archives.nd.edu/cgi-bin/wordz.pl?english=serve
Volgav vitsenanieff nivya kevach varatsach.