1 - I've worn a Nordstrom house brand crew undershirt that's mostly cotton with like 5% spandex for years under suit/tie/shirt and it's been very comfortable.
2 - I was in Japan for Jan/Feb and didn't find it as cold as everyone warned me it would be. However, that was coming from SoCal. It was cold by SoCal standards, but I spent part of my childhood in Chicago and it was not cold by IL standards. I found the subways and the insides of buildings warm. So the trick for me was to dress in normal mid-weight (SoCal) suits with normal undershirts for inside, and then have overcoat, scarf, gloves and umbrella for outside.