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Ten words put U first and D third, and six of them open with UN. That prefix is most of the page.
N takes the second box in six of the ten, sixty percent. P follows on two, and D and R take one each.
So the second box is really a yes or no question about N. Answer it and you have either the large branch or a remainder of four words.
UNDER is the common one. UNDID and UNDUE are ordinary enough to reach for. UNDAM, UNDEE and UNDUG are word game entries and none of them would occur to you unprompted.
UDDER is the obvious escape, and it is also one of the three words here that repeat a letter. UPDOS and UPDRY come from the P branch and both are modern coinages.
URDEE is the last one, a heraldic term. Between UDDER and the P branch, everything outside UN is either familiar or very obscure with nothing in between.
UNDER tests the largest branch and the commonest ending at once, since E closes three of the ten. If it comes back empty, UDDER moves you outside UN in a single step.
No, three words here repeat a letter. UDDER is the one you would actually think of and the others come from the UN branch.
The plural of updo, a hairstyle gathered up on the head. It is one of the two words here opening with UP.
It fits the letter pattern regardless of what part of speech the puzzle expects. UNDER runs U, N, D, E, R, so the D sits third.