Can I look something up while I play?

Yes: the Reference button under the question (or R on a keyboard; Alt+R, Option+R on a Mac, while typing an answer) opens what we have on the item without leaving the game: its readings and meaning, the audio, stroke order, the kanji in it, words and an example sentence, and a link to its full page in a new tab.

In practice mode it's there all the time. In every other game it appears once you've answered, so it never gives an answer away. Opened after a right answer, the game waits for you: tap Next (or press Enter) when you're ready.