How much land could a farmer cultivate, and how many people would (let’s say 640 acres or a square mile) of farmland be able to support?
Hello; I recently wrote an answer here that I hope will answer your question. It looks at average land holdings and agricultural land use based on the figures of Domesday Book.
The TL;DR of that post is that the most common land tenure is a virgate, a quarter of a 'ploughland' or 'hide' at roughly 30 acres, but a close second is a 'smallholding' which is most likely about 15 acres, but could be as few as 5.
640 acres is therefore about 5 1/3 ploughlands, and so could theoretically support 21 virgate-holding households, although it's more likely in practice that this land would support maybe 14 virgate-holders and perhaps 14-16 smallholders. It's tricky for reasons outlined in my linked post to convert numbers of 'households' into a concrete number of people, but it's estimated (very roughly) to be about 250-300 people.
In terms of how much could a farmer live off, records suggest that some more marginal smallholders - particularly 'cottagers' - held around 5 acres so... about 5 acres.