I have tried to play the first Aretha on Game Boy.
I don't recall enemies stopped spawning after reaching a certain level. I do think they even leveled-up with you.
Not unless it was an emulation bug, which is certainly possible. On VBA, the game will glitch up when trying to save. On bgb, it might with default settings. Going to the accuracy settings of the emulator and turning on SRAM Locking seems to fix it.
But speaking of pathfinding, I know I had been able to just clip right over a river to the right of the start and skip the first dungeon, which makes me wonder if the game has more bugs.
The other thing about level-ups in the first game: they don't always increase your stats. Each character is set to have certain stats rise and DROP with each level-up. The only consistant increase is max HP, which is fixed at 10 points per Level.