1) Pantherella. They do a range in cotton lisle
2) Depends.Colour is important , so much of what is on offer is dull ! Bright colours preferred. Material: cotton lisle is perfect, but expensive, I hate synthetics, some mixes of cotton/wool or synthetic/wool are OK. 'Cotton rich' I avoid.Cashmere is a joke, but someone with money must buy them! Pure wool is not as ideal as some might think: the buyer wil shrink them eventually.Length: if for formal wear they must be full calf, and that's better with a suit for business. Half-calf is OK . Shorter than that for more casual wear.
3) Less than once a month. I tend to buy a lot at a time, but sporadically
4) Yes. Your rivals online offer very little variety in colours in the 'top end .There ought to be more profit in the 'top end' rather than lines which places like Tesco sell and selling online is perfect for 'niche markets'/luxury markets where you can be a cheaper and (possibly) offer a bigger range than regular shops.! Online will get the bigger orders.Once online, the temptation is to buy more whilst 'there'.
5) No exact idea, but I'd expect to pay more than �10 a pair
6) Don't have one.If I were to buy from a 'chain' it would be John Lewis