Back in 2013, I too faced the same problem, in which my blog is not displaying properly. I found a solution for that, and wrote a page about it.
Have a look here . . http://csswish.blogspot.com/2013/12/customize-blogger-blog-for-opera-mini.html
@kashmiribora, you are right, it is a proxy server issue. Not exactly about proxy kinda thing. It is better to be called as mobile rendering of a desktop site.
try loading mobile compatible version of a site.. eg., m.opera.com , m.facebook.com like that....
thanks