If I have Zilean at a battlefield, then I play Keeper of Masks from hidden from the same battlefield: how many Keeper of Masks are made?

You end up with 3 copies of Keeper of Masks made by tokens (plus the original Keeper) — 4 total at that battlefield.

Keeper's "When you play me" plays two Reflection tokens, and each token play is a qualifying "play a token unit" event for Zilean — but Zilean's replacement is "once each turn," so it can only double one of them. That turns 2 tokens into 3 (Rule 371).

Then Keeper's follow-up — "They become copies of me" — applies to all resulting tokens, because the extra copy created by a replacement effect inherits the event's later modifications (Rule 375, per FAQ #9917/#11564). All 3 Reflections become copies of Keeper of Masks. No recursion: the copies gain Keeper's "When you play me" text, but they were never played — they entered as Reflection tokens first (FAQ #11575).

Note all four copies have Temporary (copied from Keeper's printed text), so they'll all die at your next Beginning Phase unless something removes it.