> The first problem is a non-issue. You don't need the voting machine to do the authentication if you let a human control the ballots that get stamped/marked/whatever.
The machine can register what was vote was cast at 13:42. From there, the whole idea of anonymity disapears.
> The second problem also isn't a problem
The impossibility to have the second criterion is a problem because it prevents the first criterion from being verifiable by anyone.
The second problem also isn't a problem, because the machine doesn't need to be right. The paper ballot is leading, the machine is just an indication. The ballots are still counted by hand afterwards using the normal process. That means that as long as citizens are able to review the manual counting, they don't need to know or care how the voting machine works.
And yes, that does probably negate 90% of the advantages of voting machines.