That is a great question! I honestly don't know, I have only ever heard avo/avino/geavoj (in my limited exposure via my professor, NASK participants, and a few online chats), but never a specific gender neutral singular form. I believe "avo" (only in the singular) is both the gendered and neuter forms where context indicates use. Although, honestly I have never really considered it before. Any Esperanto ninjas care to enlighten us?
I have four grandmothers. Two are blood related, and my grandfather remarried a beautiful lady (so that's the third) who happens to have an equally beautiful twin. The third grandmother is always with her twin, so her twin is also my grandmother to me and my family. Families are weird, man. :)
Do great-grandfathers count as "avojn"? How about your spouse's grandfathers? And of course, there is always divorce and remarriage to consider. Plenty of ways to have four grandfathers.
Really, I think they were trying to trick us with this one though. Esperanto needs a bit of this: https://en.wikipedia.org/wiki/Gender_reform_in_Esperanto
Yes, pra denotes a remoteness in time or relationship (originally both backwards and forwards, though this program seems to think of it as only meaning "ancient" or "antique") So praavo is great grandfather, prafiloj would be "posterity", and pratempoj is generally ascribed to "olden-times." If you want to add any more "greats" to your lineage you can then have pra-praavo, or pra-pra-praavino or (as it seem to be done most commonly) pra-prageavoj etc.
But, when push comes to shove (I dare you to translate that and keep it's meaning) they are all some variation of avo.
Oh, and one could readily refer to one's spouse's grandparents as bogeavoj.
I'm an advocate of referring to an individual family member ("Johnny, you need to have a parent come see me.") of indeterminate gender with ge- in the singular. gepatro, and geonklo, genevo, gekuzo, and, of course, geavo. But the people who put this program together are not.
Any more questions?
Aw, Esperanto is beautiful. Remember how the root "aqua" becomes "akvo"? Letter q is naturally substituted by k, and u by v. It's the same here: the root "quar-"(i.e. Latin: quattuor; English: quarter) becomes "kvar" according to the same rule. Although it might be a coincidence...?