Are there any specific design considerations that are made over nonreusable, traditional rockets to tolerate the blast from the stage 2 engine? As shown in this moment:
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The top of the first stage (booster falling to Earth) has a pusher arm which pushes the second stage away from the first stage. I assume they have calculated this to provide enough force to create a big enough gap that this doesn't affect the flight of the first stage. You can view pictures of the first stage once landed, there never seems to be any extra wear and tear near the upper part of the first stage. This indicates that its not largely affected. The distance between the two stages is probably considerably larger than it looks, would work it out but the force the pusher applies isn't known outside SpaceX, so no conclusive answer, but I think its safe to say it won't affect re-usability or they wouldn't do it. Hope this helps.
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The moment of separation of the two stages is one of the most dangerous parts of the flight. Of course, there is a system responsible for not letting two stages interfere with each other.
When SpaceX just started launching its first rockets they actually had a fail like that, when because of wrong calculations, the first stage hit the second stage(you can see it here). So as we can see, this part of the flight is really dangerous and any miscalculation can fail the mission.
So, let's talk about the technology behind the separation. Most of the rockets use either pyrotechnical detachment systems or hydraulic pusher arm. This methods help to create sufficient distance between two stages. SpaceX uses a hydraulic arm, but besides that, you can see that the booster is equipped with cold gas thrusters as well. This also help to change the angle of the boost primarily to reposition it for landing trajectory, but I believe they also take booster away from the flames of the second stage.
