not as pure mercury but you can make amalgams (like in dentistry) or alloys of some sort. You can't really change the fundamental properties of an element at a whim.
Put a lot of pressure on it
There are two possible ways to make mercury solid at room temperature:
1. You could increase the pressure around the mercury to extremely high levels
2. you could alloy the mercury with another metal. This is known as an amalgam. One common mercury amalgam is KHg, or potassium amalgam. The melting point of this amalgam is around 180oC.
In early dentistry they would use an amalgam of mercury containing, amongst other elements, tin and zinc for fillings.
I get the impression you'd need a pressure of around 12000 atmospheres to do it. There's no other way
no, that is an inherent property of the mercury, it cannot be changed.