In the end, here are the only changes (to the original theme) I did to successfully achieve what I wanted without bug:
Change container to container-fluid in header.tpl to set the "default" format to fluid.
For each page that I want to be non-fluid, wrap the whole ***.tpl into a <div class="container"></div>.
For example I did this for category.tpl, topic.tpl, register.tpl and login.tpl.
It works.