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If the freezer door is stuck shut, you'll need to unplug the refrigerator and just allow everything to thaw out. When the door won't open it means that ice has formed inside the freezer door and it's holding the door shut. Aside from physically forcing the door open and possibly breaking it, the other option is to just unplug the refrigerator and allow it to thaw out.
Yes, because if there is ice built up it stops the air from circulation properly. The refrigerator steals air from the freezer so if the air isn't circulation properly then the refrigerator won't cool properly.
You of course wouldn't be able to see it since the door is shut, but there isn't anything else that would stop the draw from opening other than if the rails have jammed up. If that was the case then you'd have to force the drawer open and replace the rails.