Is it possible for the game to generate a level with an elevator that you have no way to get to? That's what seems to have happened in my current game. Not that I mind starting over - just wondering if this is a freak occurrence or something that happens on the regular.

Well yeah, there'll be times when the elevator will be on a tiny island in the corner of the map or something. There are usually ways round this. Don't forget to walk round the edges of the map to generate new paths if there are any. Otherwise you would have to use icarus wings or get lucky with a door. It rewards thorough exploration and good resource management.

It happened to me and my sister quite a few times in the umpteen times we beat the original version. To my knowledge, there are only two solutions: icarus wings or go back down to level zero, drop off and hope you land next to the elevator. Sometimes the island where the elevator is can be reached by jumping with hi tops too. Also make sure there isn't a bridge that you just haven't spawned by walking along the nearest coastlines.

Nope it can't happen. If it appears to be on an island just walk around the edges until a pathway appears in front of you. If you can't find one keep trying and you will. Walk over every part of the edge.