Thanks for the excellent feedback!
Hit boxes have always been one of the most complicated aspects of top-down shooters. In some, the whole square-shaped image is the "hit box" and in some just a single pixel in the middle is the "hit box".
Scrapship uses both of these concepts, but ultimately I'd like to add "pixel perfect" hit detection, for the reason you just stated.
Although the entire player sprite can take damage, it's the very center of the player sprite that you want to protect at all costs.
Sounds like you found the bug where the game stops spawning enemies. If that happens you can press "3" to trigger the Battleship boss. After you defeat it, the Stat Screen will display.