Does the Skyway go directly into the Stadium so you don't have to go outside or wait outside?

There is skyway access to the stadium but you will have to go through normal security which they have setup right in the skyway just before you enter the stadium, considering the cold weather you will want to budget extra time if you plan on entering this way as it is the only heated entrance

Yes, it does. It's about a 20 minute walk from the city centre. The shortest way between the city centre and the stadium at one point cuts through a level of a parking lot (~ 30 yards) which is "open air" and the entry on the opposite side may be a bottleneck especially on the way back from the stadium, so you may have to spend a couple of minutes "outside". Also expect significant congestion (up to 30 or even more minutes queuing) when exiting the stadium through the skyway especially if your seat is on the far side. This may make you standing for minutes just a few feet away from the open large exit doors where this way it may be pretty chilly.

Yes it does