What are the best ways for making a yii1 site search engine optimized? are there any extensions that I can propagate and take my project above some levels in Search Engine Optimization?
I am eager to try every possibility and get myself in every nooks and corners and find myself a reliable and efficient solution to this. 
To optimize your website, you need to follow SEO techniques in a right way.SEO don’t depend upon any framework to get best results you need to focus on professional white hat techniques.
Yes for sure in my entire life I have always followed the white hat techniques and I hope you got me wrong here. I was asking for white hat triks and plugins that are available for checking a yii site optimized level. As like the guys in wordpress has yoast plugin. Do we have some of’em?
Yes, there are plugins and extensions available for SEO in Yii framework.To make URL of your website user-friendly, you can use these extensions.Here is the link you can check it out http://www.yiiframework.com/extension/seo/
Else than plugins you can optimize your code to get faster web page loading time and add some quality content in your website to get good results.