it should only affect the plane it is on (e.g. the x plane).
you can use a capacitor to average the readings and reduce noise.
accelerometers are great in theory, though they can be quite tricky in practice. holding them straight, 1 of the axes (usually y) will always register an acceleration due to gravity(the accelerometer isnt moving but gravity is causing stress on the microstructures causing an acceleration reading on an axis). if the accelerometer is tilted then more than 1 axis will be affected by gravity. The difficuly comes from trying to differentiate which part of the reading is coming from movement and which part is coming from gravity. If your movement make a slight tilting motion as well as a forward/backward motion then it will affect the other axes but only because the gravity reading is switching axes. Getting to grips with differentiating gravity from actual readings is essential for using accelerometers.