Is the 'big' size actually bigger?

No, it is not. I wear a size 13 shoe and this sock fits slightly snug for me. The socks would definitely not fit a size 14 or 15 foot. These socks are also much thinner than a standard Gold Toe athletic sock. The biggest problem however with these socks is that the elastic around the ankle is insufficient to keep the socks at shoe level or higher. After a very short amount of walking, the top of the sock is underneath my heel. These socks are inexpensive, because they are not well made. Consider another product.

Is the "6 pack" 6 pairs of socks?

Yes. The six pack is 6 pairs of socks.

Where are these made?

75% Cotton, 19% Polyester, 5% Nylon, 1% Spandex

what is a liner sock and how is that different from a sock?

It is thicker from toe to heel. A regular sock does not have that added cushion and protection for wear and tear. These are by far my husbands favorite socks.