

This is one of the few swaps that is a real privacy upgrade. Zcash can be private, but only inside its shielded pool, and only if you deliberately keep it there — most ZEC in circulation, and almost everything that touches an exchange, is transparent. Monero removes the "if you remember to": every transaction is shielded by default. Moving ZEC into XMR trades optional privacy for automatic privacy, with no account.
One honest wrinkle specific to Zcash: whether this swap improves your privacy depends on where your ZEC was sitting. Here is how to swap ZEC to XMR on XMRS, and how to think about it.
Either way, the destination — Monero — is private without any special handling. That is the point.
Timing follows Zcash confirmations first, then the Monero payout; most swaps finish within 20–60 minutes. A promocode lowers the exchange fee.
For the default case, yes. Monero shields every transaction automatically; Zcash makes shielding optional, so much of its activity — and most exchange flow — is transparent.
No. Transparent ZEC behaves like Bitcoin and is fully public. That is exactly why swapping into Monero is an upgrade.
Dash carries an even weaker, optional privacy model — see XMR → DASH for that discussion.
Use XMR → BTC whenever you want Bitcoin.