The answer varies based on time and certain variables (such as weather, disease, health, technologies, etc). It's almost impossible to calculate universal answer because the answer could vary though out time

Engels in his book on Macedonian logistics calculates that each man needs 3lbs of a wheat ration per day (wheat being the primary foodstuff). Roth in his work on Roman logistics estimates a 1.1-1.3kg worth of food (grain, vegetables, meat, etc...) which works out to around 2.5lbs (ish). Now this is for an army on campaign, I'm not sure if there'd be a quantitative difference for soldiers in garrison.

Of that 1.2(ish) kg of daily rations in Roth, 850g of that is grain. So that'd be 310.25kg per person per year. So for 1,000 soldiers that's 310.25t of grain over a year.

Now from some source on agriculture (I'm sorry I don't remember where these numbers came from, so caveats and all that), 1 acre produces 10 bushels of grain and each person needs 20 bushes per year. But half of the fields are fallow each year so you'll need a total of 4 acres. Now throwing 20 bushels into this converter I get 544kg for wheat and 308kg for oats. So oats seems to match Roth's calculations despite the Romans primarily consuming spelt which is a form of wheat.

So it seems 1,000 soldiers would need to be supported by 4,000 acres of land just for the grain portion of their diet. Make of that what you will.

As for your last question, that heavily depends on the period and the locale. With early-middle Republican Roman and the Greek classical city-states, recruitment depended on land qualifications. You needed to have enough land to be able to support your family and buy all the arms and armour to serve, poorer men were effectively excluded from military service and all the political rights that came with it (though some did serve as light infantry but battles were very rarely decided by them).

Now Athens mustered 10,000 men for Marathon when their very existence was at stake. Half a century later Thucydides says Athens had around 29,000 hoplites of which 13,000 were available for campaign (the remaining 16,000 were the oldest and youngest who performed guard duties on the walls). Considering Athens has (according to this site) 618,000 acres of arable land (enough to support 150,000 people @ 4 acres/person) and still needed to import large amounts of grain from the Black Sea region, that means a population well over 150,000... I don't think anyone knows what that number was though.

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