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Seventeen words put N first and N third, which means every one of them uses the letter N twice.
O takes the second box in six of the seventeen, with A and I on five each and E on just one. Only vowels appear there, and the branches are small enough that the second box rarely decides anything.
NANNY, NINNY and NONNY put a third N in the fourth box, which makes them the three entries here that repeat a letter. All three end in Y, so a double plus a trailing Y narrows the page to those alone.
NINTH, NINES, NANNY and NINJA are the entries most people would produce. NONCE and NONET are reachable at a push, and NANDU, NINON, NONYL and NENES are not.
S closes five of the seventeen, twenty nine percent, with Y on four. Between them they take most of the last box.
E leads the fourth box on four words with C and N on three each, so nothing there is decisive.
They share three letters and split at the fourth box. NINTH is the more common word and its H ending appears on only one entry here.
Yes, it runs N, I, N, J, A. The J in the fourth box is unique on this page, so guessing it either wins or costs one turn.
A large flightless bird, also called a rhea. It sits in the A branch with NANAS and NANCE.