Correct me if I'm wrong, but I'm pretty sure you have to reset the Tamagotchi to go into debug mode. After you put the battery back in, you will be prompted to chose between reset and download. I'm not sure if anything weird happens to your data if you click download. Also, in debug mode you lose the ability to connect to your PC, but Tama Town has been down for years, so that doesn't affect anything.
Of course you could always risk damaging the Tamagotchi in the debugging process. Just be gentle when doing so. If you don't want to risk breaking your Tamagotchi or losing your save data, I'd recommend you don't debug it.
As for the death thing, the exact requirements for the Tamagotchi to die on the V3 are (
sourced from here):
- Getting sick 4 times in the same growth stage
- Staying sick for 12 hours
- Having 0 hungry hearts for 12 hours
- Getting 5 care mistakes in the senior stage
It probably got sick to many times, or maybe the Tamagotchi glitched. I've heard that on the connections (particularity the V4) they become glitchy when the batteries are low, and that can lead to the Tamagotchi suddenly dying. I'm not sure if weight has anything to do the Tamagotchi getting sick or dying on the connections, but I do know that it does affect the bump minigame. (Higher weight = More likely to win and less points earned, and lower weight = Less likely to win but more points earned.)
