Why is 'will you buy' not accepted?
That's an odd way to phrase the question. 'vil' should in most cases translate to 'want to', especially if you want to know what the other persons wants.
Am I right that both 'pillows' and 'putene' in these examples means bed pillows and what we British call cushions, rather than just for bed pillows?
Both 'pillow' and 'cushion' are accepted translations.