Regarding your first point, Eratosthenes never used or heard of miles. The mathematics of his experiment carry the unit through to the end result so he could have used any measurement he wanted. Potential candidates include Wagon-Wheel Diameter, Bunny-foot length, or his least favorite cousin's armlength. He probably used a unit called the Stadion, but modern modern authors simply converted his end result to Miles for the modern retelling.

Regarding the second point, his mathematics would work perfectly if the sun's light was collimated and the Earth was a sphere. Neither of these things are true in reality, but they just happen to be approximately accurate, which is why his result was so close.

I'm not sure I understand the problem here. It's completely inconsequential which unit of measurement Eratosthenes used and which was presented to you--units of measurement can be converted perfectly fine. One meter is the same as 3.28084 feet, but the conversion doesn't change the amount of distance being described. In point of fact, no, Eratosthenes of Cyrene didn't use miles as his measurement. Eratosthenes' calculation is preserved (it is most certainly not "legend," being originally published in Eratosthenes' now-lost Περὶ ἀναμετρήσεως τῆς γῆς, "On the measurement of the Earth" and then probably again summarized in his three books of Geography) in both Cleomedes and Strabo. Eratosthenes, like Greeks generally, measured large distances in σταδία, a measurement around 200 meters. Thus Eratosthenes' measurement of the circumference of the earth was 252,000 stadia, around 45,460 km. You've merely been presented a conversion into miles for convenience, the difference in precisely what unit is used is meaningless and changes nothing. In point of fact, the mile did in fact exist in antiquity as a unit of measurement used by the Romans, but the Roman mile (measured as being a thousand paces, hence its name) was some 142 yards short of the standard English mile.

Whether Eratosthenes personally believed his calculation to be perfect (which I would consider extraordinarily unlikely) it was not accepted as gospel by everyone. Strabo famously preserves most of Hipparchus' arguments against Eratosthenes' geographical calculations in general, and Hipparchus' treatise on geography was probably basically a polemic against Eratosthenes, whose geographical work did not merely comprise a calculation of the earth's circumference but a great deal more as well. Hipparchus' calculations, as quoted by Strabo, are largely not significantly different from Eratosthenes' but are much more precise--the entire basis for Hipparchus' transformation of astronomy from the theoretical to the practical was his introduction of methods of much more precise calculation.

According to "The Mapmakers" by John Noble Wilford, he actually made several mistakes, some of which cancelled each other out:

1. He assumed the earth was a perfect sphere (didn't make a big difference).

2. Syene was not on the the Tropic of Cancer as he assumed - it was 60 Km to the north.

3. Syene and Alexendria were not on the same meridian with Syene being 3.3 degrees to the east

4. The distance separating the two was 725 kilometers apart instead of 800

All of these things were actually pretty difficult to measure those days and he relied on travelers and did not make the measurements himself. However, the theory behind his approach was pretty dead on and if he was confident in that, he was probably confident in the results.