Never mind... I figured it all out!
a)
$\displaystyle v = \frac{dx}{dt} = ln(t)$
b) The particle will be moving left when v > 0. So when is this?
c) To answer speeding up or slowing down you need to look at the acceleration. Have a care: look at the magnitude of the velocity when you take your derivative because the question is not asking if the velocity is increasing/decreasing, it is asking about the speed.
-Dan