Could you explain how to change the width of left and right position in canvas ?

You'd need to modify the PHP of the template. It specifically calculates what Bootstrap column class it should use so you'll have quite a bit of usage to change. The PHP file can be found below.

components/com_comprofiler/plugin/templates/default/default.php

Changing the width in CB configuration does not seem to work for canvas with two columns, do I have to manually change bootstrap.css for this ?

That's not for that position. Those widths are for left, middle, and right positions an not the canvas ones.

I have also tried to set the connection tab to right position but the button is getting out of the screen. Is there a possibility to make it float ?

The Connection Path tab won't fit there, it's designed to be a header like banner. You'd need to restyle it to have a different usage.