the orange tree you thought had "sprouted" was probably dead and you just couldn't tell the difference. when you plant them, and they're successful, the next day it will look like a little branch with a pompom on top of it. if the leaf is leaning to one side with what seems to be a bug bite on the leaf, it's gone to tree heaven. if it disappeared after 2 days, it did die unless you time travelled back before you planted it, but you said "the day after it sprouted it was gone."
the only things specific for your trees is that you don't place them right next to anything - like a rock, house, river, the town gate... even diagnonally right next to something, it will die 100%. trees need to be planted 2 spaces away from anything to grow.
they will also 100% die in certain places in your town because there are some places that are "reserved" for things like fossils and events that happen in the game throughout the year - like where the guy stands to judge your fish during a fishing tournament. there's no way to tell if a spot is a doomed spot unless you plant a tree there, it's not 1 space from something and no one ran over it.
you do not have to water your trees to grow, although they will die 100% if you RUN on them. i don't even walk near mine when i plant them, lol. they also won't grow any faster if you water them.
coconuts will only grow 7 spaces away from the ocean, so don't plant them anywhere else throughout the town or they'll go to coconut heaven.
fruit trees will be fully grown and will have fruit 4 days after planting them.
furthermore, even though these aren't fruit trees - cedar saplings (christmas tree looking trees) will only grow on the UPPER level of your town (not where you walk down the ramp to go to the bottom level), although i have some cedar saplings growing around my ramp, so that's possible.
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