Don't confuse transactions with settlement, this isn't bitcoin we don't reference previous TXs, when building new TXs. We just have accounts with summary balances and this means that individual transaction histories are default private.
Settlement happens once a week and it's always mint to mint and yes settlement requires a majority of mints to sign off. Refusing mints are penalized by not being able to exercise TRs until they sign off, since all TRs must reference the current settlement proposal as supported by the majority. This means if they want to pay bills, they'll need to buy coin on the open market.
For individuals and businesses though, transactions are instant and all accounts are multisig.
You sign a transaction that amounts to "move x units of VIVA from account A to account B" and submit it to whichever mint happens to be handy for you.
The mint verifies you had the authority to authorize that movement (you are the account owner, or you had their permission), and then countersigns.
This transaction is added to the local chain of that mint, which will generally be instant. From here your summary balance is updated and begins to percolate through the balance chain (summary account balances are maintained on a separate chain that has a 1 year rolling window).
If account B is not with your particular mint, then your mint transmits the B side receipt to B's mint (source is left blank unless you specify otherwise).
Both mints sign a "movement receipt" / slip which shows the mint to mint action and the movement slip is broadcast to the network. The sum of movement slips is what is factored into the initial conditions of the settlement procedure.
A movement slip is always a debt between two or more mints.
Transactions between individuals are considered private and never broadcast to the world.
You don't need all nodes to be active and you are free to move your account from one mint to another for any reason at any time and no one can stop you or freeze your account.
Authority, i.e. individual account ownership certificates, are kept in the CAN, and change deltas such as issuing and revocation of certificates, form their own individual chains similar in many ways to Git or IPFS.
You can add or revoke authority for any cosigner at will. But mints are liable for every penny they sign off on. Thus you have the irreversibility of bitcoin, i.e. recipient is never liable for chargebacks, with the advantages of more civilized methods of payment like bank accounts, where you can dispute transactions and you have a window for doing so.
Mints must also produce on demand by you, your personal transaction history if there is a dispute and they must be able to justify any balance changes by providing the A side on demand. But you have to demand it. Otherwise your history is invisible to the rest of the world.
I think that this explanation about relationship between Crown Holder, Mint and worker require an independent post with more diagrams and numerical examples, for nongeeks.
Thanks for the detailed response, I will keep an eye out on the project