To explain, point 1
Potentiometers have three terminals, the two ends of the resistance, plus the slider. Make sure that you know which terminal is which on the old and the new and that you connect the slider of the new one where the slider of the old one went.
The two ends are sometimes marked "CW" and "CCW" for clockwise and counterclockwise. If you mix them up, the circuit will work, but the control will go in the opposite direction to the one expected.
Point 2.
Like all resistors, potentiometers have a power rating. When you put a voltage across a resistor, current flows and electrical power is converted into heat. Resistors and potentiometers have a maximum amount of heat that can be convected or conducted away before they get too hot, so generally you shouldn't replace a resistor with one of a lower power rating. However many resistor and probably most potentiometers are not used anywhere near their maximum power rating.
If you can, work out or measure the maximum voltage across the potentiometer. If not use the maximum circuit voltage. Take that number, square it and divide by the resistance of the potentiometer to give the heating power. If that is much less than the power rating of the potentiometer that you intend to use, you are probably safe.
For instance, if you have a 5 V circuit, and a 10 kOhm potentiometer, the value comes to 0.0025 W, so it wouldn't matter if you replaced a 1 W potentiometer with an 0.25 W potentiometer in that case.