The preprint for this file is: <a href=http://arxiv.org/abs/1202.4355>Low Degree Places on the Modular Curve 
X1(N)</a>, specifically the table on page 4. The answer to Question 1 on page 2 is no.
</p>
Maarten Derickx made a lot of progress on this topic since then,
see his slides "Finding all points of degree < gonality on Y1(N)" from Oct 30, 2013
on his <a href= http://www.mderickx.nl>website</a>.
He managed to prove completeness for a number of values of N, see
page 21 of his slides for an overview of the current status.