2/2 So there are no “private transactions” as in Zerocash protocol. And transactions with a zero-knowledge proof are more computantionaly expensive, and weight more than regular.
1/2 The privacy on PIVX is implemented as a Zerocoin protocol. That said, you can destroy a specific denomination (e.g. 1 coin) and then mint the same amount as a new coin.
I can 2nd that. In PIVX you "burn" a coin. That gives you a cryptographic "ticket". You then keep the "ticket" as long as you want, then hand in the "ticket" for a new minted coin.
The newly minted coin then has no history. It's so simple and elegant. PIVX didn't invent this, but they've successfully implemented this in the code, and that says a lot.
PIVX's PoS system allows for greater decentralization and equitable block reward distribution. PoS is also not vulnerable to 51% attacks. https://blockonomi.com/51-attack-calculator/
This mint and spend system can result in tx's that use multiple denominations and thus cost multiple of 0.01 PIV, but reverse is true, can get multiple anonymous tx's from a mint.
Yes, PIVX has privacy opt-in. Regular tx costs can range from free to the 0.0001 standard fee. SwiftX is 0.01 PIV for instant confirmation. Each zPIV denomination mint costs 0.01 PIV.