About the left and right side of the brain If you are right-handed person, does it mean that you often use left brain (the left part that contain analysis, language etc.)?

If you often use right leg being crossed over left leg, what part of the brain do you use? Maybe left brain?
Persons of each handedness use both hemispheres of the brain.

If you're asking specifically whether taking an action with your right hand preferentially activates motor control in the left hemisphere, the answer is yes. Motor function for the right side of your body is mapped to the left side of your brain, and vice versa. So for crossing your right leg over your left, that specific action uses your left brain to move your right leg. But that does not mean a person who crosses his or her leg right-over-left all the time is a "left-brained" person.

"Analysis is left-brain" is a pop psychology myth. A specific capability may be found in one place (e.g. speech production in Broca's area, which is often in the left hemisphere), but higher-level functionality like logical analysis or creativity have been found not to be lateralized (i.e. not fixated in one hemisphere or the other).

Nielsen, et al. 2013. "An evaluation of the left-brain vs. right-brain hypothesis with resting state functional connectivity magnetic resonance imaging." PLOS ONE