The sentence containing たく山 should be changed to contain たくさん.
沢山 is たくさん in kanji, so it’s not wrong
It’s because you haven’t encountered 沢, and they think it’s better to have some abomination words instead of using either all hiragana or all kanji.
Well, it’s not a mistake, but I’d hesitate to say that it’s not wrong.
wはt ど よu めan it’s のt wろng?
It’s not a standard way to write it generally, but it’s also normal on WK, where the context of writing that way is established as the internal standard.
Seeing half kanji words does happen for natives, but it’s usually in a school situation. What makes たく山 feel weirder in that regard is that it’s a “usually kana only” word, so even in school they would just use kana only.