SteveC said:
1. What kind of an attack does a monk have?
A monk uses unarmed strikes, which follow the rules for manufactured, not natural, weapons (specifically, as regards two-weapon fighting and the availability of iterative attacks).
2. How would a monk's attack have to be worded to make it apply to Improved Natural Attack?
In order for a human monk to qualify for INA, humans as a race would need to have a natural weapon - they'd need either a bite, a claw, a slam, etc., or the unarmed strike would need to be designated as a natural weapon.
If unarmed strike was a natural weapon, then humans would always threaten inside their reach, would generally not provoke AoOs when making unarmed attacks, and, among other things, wouldn't need the Improved Unarmed Strike feat. Moreover, they could freely mix their unarmed strike with manufactured weapons in a full attack action (even when using sword-n'-board, TWF, or two-handed weapons), and would not benefit from iterative attacks from high BAB with their natural weapon.
Unarmed strikes are not natural weapons, however. You mix them with other weapons using the TWF rules, you do not natively threaten with them, they do nonlethal damage as a default, and you may gain iterative attacks with them via high BAB.