How did he get the gun on the plane?

I was wondering that myself but that could have been a bus station or train station. Not sure if they go through your luggage when doing that.

The part that bugged me the most is that when he arrives he takes a taxi to that building but then he is shown walking to the woman's house. He surely wouldn't have walked there or taken a bus since he had the tons of money for another taxi ride to her house. I get that they wanted him on foot so the car could chase him for the story but jeez, get inventive. Figure out how to do it in a sensical way.

I assumed he had bought one locally.

Does canada have a waiting period to buy? He didnt use it much, in the woods he went for his trusty hammer. So he walked from the city to the countryside, happens all the time, not.

or how'd he get Aleksander's phone number? maybe I missed it.

Plot hole - Aspect of a film that is misunderstood or missed while using your smart phone.

He went by train. They don't check as closely when you board a train. At least they didn't used to.