It is my assumption that an America that has been overhauled, would have UBI. Thus free smartphones, because they make it easier for people to do stuff. Anyhow...
1: Open-source means anyone can look at the code, be it on their machine or at the repository. With things like hashing, it can be verified at each step of the voting process that the vote remains intact by auditors. The voting software should be device agnostic, and be something used in all elections and voting. By making the software itself uniform each year, it is easier to notice when something is off. This is very different from Diebold and other physical devices, because those are black boxes.
2: The receipts are not about anonymity. They are laminated so that people can keep them in storage, and bring them to a poll verification booth if the call goes out. The digital vote is anonymous when cast, the physical ballot reserved for when volunteers are willing to reveal their vote in public. While obviously not fool proof, it is an extra step against corruption if needed.
3: Obviously, there would have to be laws against corruption to go with a redefined nation. Also, a UBI-based society would have less corruption, because money is associated with luxury, rather than necessity. The punishment for being bribed to vote for an interest, could be to have UBI income penalized. UBI supplies, such as beds, food, housing, internet, ect, aren't taken away - just the money for buying fancy stuff that UBI doesn't provide. People who are greedy, would have to think about whether they want to lose their guaranteed income for a potential bribe.
4: When it comes to calling for a recount, it could be something like 20% of previous participants of a voted measure calling for it, or 30% of eligible voters, whichever milestone is reached first. Presumably, frivolous calls for a recount would automatically fail if they haven't garnered support. Presumably, the open-source voting software would be used for collecting the voting metrics.