Is Mercury's core liquid? A very basic question, but one to which I keep finding different answers: does Mercury have a liquid core, or is it all solid? Whatever the reason, what are the causes of it being so?
It's liquid.
As detailed here,

To figure out whether Mercury's core was liquid or solid, a team of scientists led by Jean-Luc Margot at Cornell University measured small twists in the planet's rotation. They used a new technique that involved bouncing a radio signal sent from a ground telescope in California off the planet and then catching it again in West Virginia.
After 5 years and 21 such observations, the team realized their values were twice as large as what would be expected if Mercury's core was solid.
&quot;The variations in Mercury's spin rate that we measured are best explained by a core that is at least partially molten,&quot; Margot said. &quot;We have a 95 percent confidence level in this conclusion.&quot;

The NRAO has another article on it, which goes slightly more in-depth into the subject.
The official site of the Messenger mission is slightly more cautious:

However, these constraints are limited because of the low precision of current information on Mercury's gravity field from the Mariner 10 and MESSENGER flybys. Fundamental questions about Mercury's core remain to be explored, such as its composition. A core of pure iron would be completely solid today, due to the high melting point of iron. However, if other elements, such as sulfur, are also present in Mercury's core, even at a level of only a few percent, the melting point is lowered considerably, allowing Mercury's core to remain at least partially molten as the planet cooled. Constraining the composition of the core is intimately tied to understanding what fraction of the core is liquid and what fraction has solidified. Is there just a very thin layer of liquid over a mostly solid core or is the core completely molten? Addressing questions such as these can also provide insight into the current thermal state of Mercury's interior, which is very valuable information for determining the evolution of the planet.

At this point in time, though, all evidence indicates that Mercury has a molten core.
As userLTK pointed out, lower pressure inside Mercury makes it easier for the core to stay liquid at lower temperatures.