correct, there is no such thing as change outputs. But if we create standard denominations (1k, 5, 10k, 20k, etc.) then we could treat them like dollar bills. If I owe you 50k, I could give you 3 20k utxos and you could give me back a 10k utxo if you already have one 

 I was thinking if it would be possible something like deposit btc in a musig 2/2 similar to this, all txs in the service being custodial ecash with any denomination, and every 24h or so onchain settlement with a batch tx. Keep in mind that my knowledge about bitcoin technical is very limited so sorry if this sounds retarded.  

 > This would have to be used for higher amounts correct?

Since the last holder of the coins has to create one or possibly two base layer transactions to withdraw them, I don't think it makes much sense to create statechain utxos with a value lower than the cost of two transaction fees. And let's suppose transaction fees are $5 apiece. You might think "ok then the minimum value of a statechain utxo should be $10." But that would mean half the utxo gets consumed as fees (assuming a cooperative withdrawal) or up to the entire thing (if he has to do a unilateral withdrawal). If you want to keep 99% of your money (or 98% in case of a unilateral withdrawal) then the minimum reasonable size of a statechain utxo is $500, that way you'll still have $495 in case of a cooperative withdrawal (99% of $500) or $490 in case of a unilateral withdrawal (98% of $500).

> I would not think you can make payments for 5 dollar values then right?

Under these assumptions, that sounds like a reasonable conclusion. Of course, right now, transaction fees are only like 50 cents or less, so utxos as small as $50 make good economic sense for now. 

 > Does it have a proof of reserves (or proof of liabilities?) scheme to verify the funds of the mint?

Yes, it's already built into the client. For each of your statehain utxos you can click "show info" and it will show you what bitcoin address those coins are located in, which you can verify by looking up that address on your node or on a block explorer. No rehypothecation -- you hold a key to that address, and you hold a "backout transaction" which you can broadcast after a timelock if the mint goes down. (You can see the mint's signature for this transaction in "show info" as well.)

> can this scheme be rolled everyday instead of every 30 days?

You can roll it every second if you want to. You yourself audit your own coins as often as you want. 

 To make this easier, today I added a "Proof of Liabilities" button which only shows you information pertinent to proving that (1) an address on bitcoin has enough money to pay you your liabilities (2) you have a key in that address (3) you have enough signatures from the operator to let you withdraw your money unilaterally after a timelock

These items are sufficient to prove that the reserves exist and that the liabilities toward you exist...but they do not prove you will actually be paid, because a malicious operator could steal the money from the proof_of_reserves address with help from a prior holder of your statecoin