Obligatory plug for the vocab sheet; the correct definitions should already be on there!
As for your question, this book only uses kanji at the grade 1 level. So words that are usually spelled with kanji (ไธ็ฎๆฃ) would only include the kanji that a grade 1 student knows. That does confuse jisho sometimes, so yes, try the hiragana version and usually that comes up with the right word.
Hmmm, are you looking for manga or for prose/stories?
For manga, most of the ABBC picks should use standard kanji spelling, but would have furigana. The BBC will sometimes read easier manga with no furigana.
If youโre looking for stories, the 2nd grade readers would have more kanji (up to the required 2nd grade kanji knowledge of a Japanese student), but wouldnโt use standard adult spelling. Childrenโs novels also use more kanji, but spell some words with hiragana. Checking the BBCโs past entries, this club looks like it read a book that may use more kanji.