The range proofs are verified by monero nodes or the transaction is invalid, so it is sort of like asking to audit that all bitcoin transactions are correctly signed. The cryptography for Bulletproofs and its implementations are audited by cryptographers, which you can read. Just run a monero node and count up all the inputs from the block reward, which are public. That's the supply.
>It's a crypto-asset that's optimised for storing large amounts of value of large amounts of time (similar to gold, but much improved).
The low block size and resulting high fees aren't an intentional design decision. It's not "optimized" for anything except the network conditions of 2010, because that's the last time satoshi changed it. Satoshi clearly intended for the block size to be raised[0][1].
The difference between gold and bitcoin is that gold doesn't require a constant value transfer to miners (in the form of inflation or fees) in order to be secure, gold can just sit in a vault. In 10 years down the line if the mining reward is too low (coinbase keeps getting cut in half, transaction fees will need to increase to accommodate), miners will sell off equipment and attackers can buy them up.
it recreates money printing unless you are using lightning. If it is just some payment processor you don't have a payment channel with (like PayPal as you suggested) there is nothing stopping them from doing fractional reserve banking on the other side and giving out loans.
People can self custody now because fees are low. If more people use bitcoin, the fees go up and it becomes impractical. Using bitcoin for everyday transactions is the whole point bitcoin was created in the first place.
>In addition, it is fully auditable, meaning you can have your bitcoin fully or partially custodied by a third-party but have full access to the public keys for the bitcoin wallet, proving your money is where the custodian says it is. yo This will just give you proof that the custodian hasn't moved the outputs, which is sort of flawed. It doesn't tell you anything about ownership.
[0] https://bitcointalk.org/index.php?topic=1347.msg15366#msg153... [1] https://bitcointalk.org/index.php?topic=149668.msg1596879#ms...