Translation:The field was bought by the angry old farmer.
The field was purchased by the angry old farmer." is actually slightly more common and correct. It should be accepted also.
I would think ' the land was bought from/of ...' and that means the opposite of 'by'. An old farmer buys no more land, he dies.
Is "to buy sth OF someone" correct English? I'm not a native so just wondering :)
No. You could say 'I bought this fish off the market' but in most cases you'd say 'buy something from someone' e.g. 'I bought sweets from the shopkeeper'