Why do we knock our heads, cross our hands to catch the ear tips and do the squats (Thoppukarnam) in front of Ganapathi in particular?

Purpose of visiting Ganapathi is to help improve our brain power.  In America and Japan, they call our thoppukaranam as Super Brain Yoga. See this 15 year old American video to understand more.  https://www.youtube.com/watch?v=KSwhpF9iJSs

In our gurukul days, Gurus used to make kids do this. It was never a punishment, but ways to increase the neuron actions in the brain by pumping more blood to brain.  So, they used to pinch the ear tips, not to cause pain, but to pump more blood to brain.  Same is the case with knocking on foreheads, it disturbs the set patten of rhythm in brain and helps developed new connections within and helps lateral thinking (out of the box new ideas).  As Ganapathi represents brain and we go to him to solve problems, these are done mainly infront of him.