I will be the contrarian: JSON numbers are not floating point values, they are strings of characters matching the format "-?(?:0|[1-9]\d*)(?:\.\d+)?(?:[eE][+-]?\d+)?". You can choose to parse them however you want, and parsing libraries should provide a mechanism to decode to an arbitrary-precision value.
By way of example: when I worked on payment code in Java, we accepted numeric JSON values in request payloads but they were deserialized into "BigDecimal" fields in our payload classes, not "float" or "double".
Luckily, there are not many broken JSON parsers out there, as this is a well-known issue. Just about the only parser that remains broken is Javascript's JSON.parse(), because it doesn't allow for any options to control the parser, which is why we keep having this discussion.
Yes, because JSON.parse() treats the input as if it were a JS object literal; that is, JSON.parse(JSON.stringify(someObject)) will be idempotent. Usually parser libraries let you construct a parser with options, so you'd make a "let json = JSON({parseNumbersAsBignums: true})" and use that everywhere, but JS doesn't have that built in.