I just started katakana and it showed me how to spell cake. And now I have an idea for a hanko, but if I can spell it in katakana could I just use hiragana with the same sounds? (What I mean is basically are words spelt with the same sounds in both katakana and hiragana?)
The sounds are the same, but some words are typically only written in Hiragana (おもしろい), some only in Katakana (ケーキ), some can use either (ドキドキ vs どきどき), and some use both at once (e.g. ラーメンや).
There's technically nothing stopping you from writing けえき instead of ケーキ, but that's not the *normal* way to write it. As a beginner, the general advice is to use whichever alphabet was used when you first learned the word.