I'll give you a hand at editing.
One morning, Lindi found an elephant in her room.
>>I'd also say "tenpo wan pi suno kama" or "tenpo wan pi sewi suno" for "one morning", but those might not be necessary. I do think of "one tomorrow" when looking at the initial translation (or some such thing). I reckon "jan Linsi" would be the way to go - it's sticking with the usual way to transliterate "ti". I also think "ona" is pretty clear in this case myself.
“No there isn’t,” her mother called back. “Elephants don’t live in houses. Everybody knows that.”
>>I think "mama meli" would be good, just because there's a "mama mije" later on and it helps. Personally, I'd regard "toki sin" as "spoke again" (as if she said something earlier) or "spoke newly" (gah English) (as if she was starting a new conversation almost), so I think that the original is fine here.
The elephant yawned.
>>I might personally use "kama jo en pana e kon" just because both happen at pretty much the same time, or else in a very one-after-the-other manner. I know tp is tp, but personally I only see "kama jo e kon" as an inhale (but that might just be because I've used it in my own writing that way before and haven't considered much else).
The elephant burped.
>>This is my own perspective, but "pana musi e kon", "pana e kon nasa tan uta", "pana e kon jaki uta" etc could be viable here.
At school, the teacher grumbled, “What’s wrong with this chalkboard? It’s all wrinkly!”
>>Personally I'd say "sinpin sitelen pimeja" for a blackboard (remember, it's probably a whole wall length, upright, and definitely not bendy). I'd also recommend "anu seme?" and "tomo pi kama sona" and "jan pi pana sona".
“That’s not the chalkboard. That’s my elephant!” said Lindi.
>>*"soweli suli mi!"
At break time, the elephant followed Lindi to the playground.
>>I reckon you can merge your edit idea with the original as so: tenpo musi la soweli suli li tawa ma musi poka jan Linsi. Still doesn't quite imply "follow", but maybe someone else can come up with something for that, or maybe it's not necessary.
The elephant drooped. He walked away, wiping his eyes with his trunk.
>>Probs "ona li tawa weka". Maybe for the last bit: "ona li weka e telo tan (sinpin/sike lukin/oko) ona kepeken luka linja ona." (That's if we stretch "luka" to be some kind of grasping appendage rather than just a human arm, and also assume that the audience knows by this point that an elephant is in question. Otherwise it's probably better to just mention tears and nothing else.) I personally don't see "oko" as too bad a habit. If "oko" is a bad habit, then so is "uta" and "noka", I reckon.
Back home, Lindi didn’t want to play, or read, watch TV.
>>While your points hold true, I reckon that you can at least say "wile ala lukin e lipu e sitelen tawa" to condense it at the end.
She felt lonely.
>>Personal favourite out of those two is "taso pilin", as I think it's stronger, and "wan pilin" could still have a sense of feeling united with everything (oh the intricacies of tp numbers...)
So she went outside, and sat on the steps, and waited.
>>I'd say "tawa ma" could be an option (though maybe not needed in this case as she's close enough to the house that it could be "tawa selo tomo").
>>I think "ona li awen" is plenty for both lines (or maybe even "ona li awen. / ona li awen awen.). "sin" is a sense of "again" or even "newness", so I don't personally see it as fitting here unless she does something inbetween waiting.
And then… she saw a trunk.
>>Similar to my last suggestion, maybe "luka linja" could be put into use, as "nena" is not "linja" or "palisa", which is what the shape takes after in an elephant. I don't get what "wawa la" is personally. I don't even think "And then..." need be translated, but that's just me.
>>Or "palisa uta kiwen tu"? Just playing with words here.
>>Fear not, "nena kute" (or "lipu kute" for an elephant perhaps) could easily replace just "kute".
She waved to her neighbours. “Hello, Mr Green! Hello, Mrs Green!”
jan Linti li lukin e jan tu lon poka e tomo ona. jan Linti li toki e ni: “jan Laso Mije o, toki! jan Laso Meli o, toki!”
>>I reckon "jan poka tu" sounds good (or maybe "jan tu pi tomo poka"), it could be a new term alongside "jan sama", "jan pona" etc. I definitely think that "mije Laso o, toki! meli Laso o, toki!" is the way to go (or maybe for added politeness, "mije/meli pona Laso"). Just realised - wouldn't green be closer to "jelo"?
“Look at Lindi!” said Mr. Green. “How did she get up there? Maybe she grew!”
jan Laso Mije e toki e ni: “o lukin e jan Linti! ona kama sewi tan seme? kin la ona li kama suli!”
>>"kepeken nasin seme" could also work, since it's pretty ingrained as a "how".
“Don’t be silly,” said Mrs Green. “Little girls don’t grow that high. Everybody knows that.”
jan Laso Meli e toki e ni: “o toki e nasa ala! jan lili li kama suli mute ala. jan ale li sona e ni.”
>>"o nasa ala" sounds good to me
Maybe that part can just be reworded as "jan lili meli li ken ala kama suli sama ni." (Little girls can't grow as high as that, kind of a thing.) (Using "ken" to avoid "kama suli mute/kin ala" etc, but then again, some problems must be faced)
The elephant took her to the lake, and Lindi slid down his trunk like a slide.
>>I see what you're doing there, but I'm not sure how clear it is, especially since "telo suli" could be taken as some kind of adverb system for "tawa". If other people think it's ok, though, that's all goods.
They played all afternoon, laughing and splashing and spraying each other with water.
>>Afternoon could be "suno li kama anpa tan sewi/suli ona la", though it's a little idiomatic I suppose (When the sun descends from its height). Noon would be more "suno li sewi (kin) la" probably. I reckon "tawa (wawa) e telo li telo musi e ona (tu)" could sound a little nicer than "pakala e telo", but that's only my perspective.
That night, the elephant tucked her in to bed.
tenpo pimeja la soweli suli en jan Linti li tawa supa lape. soweli suli li pana e len lape lon jan Linti.
>>Probs "pana e len lape tawa jan Linsi".
He patted her head, and curled up to sleep outside her window.
soweli suli li lape poka lupa tomo pi jan Linti.
>>Then how about "luka e lawa ona"?
And finally, a message to jan Same (if you see this): I love how you translated certain parts of the text! It's so cute and a wonderful story to have in Toki Pona.