Praveen, there is nothing wrong with Moodle, or Essential Theme that you are using, that could drag your site down, but with your own development.
Second, the images that you have been using + going to use in future, are NOT web optimized so to speak. Just dragging and dropping the images for a web use is not a good practice to speedup the sites.
Third, you haven't even started putting courses in your website, and you have plenty of Bells & Whistles added to the code. Things like Addthis social icons, Feedbacks and user Alerts coming in from all 4 corners of the website, I am not deviating from the use of all these on the website, but right thing at the right time. If you want to keep all these things intact, then best solution for you would be installing Moodle in a sub directory like www.mydomain.com/moodle and use index page on root of domain that shows a welcome message of a logo with auto-direct to the moodle site. This is the best way to tackle the web page response if you have heavy content....take example of Google's home page, or Facebook's home page. how heavy they are?
and Lastly, the money you've put in buying WebEngage, rather put that money into getting a CDN service. The Test you performed may have servers in US, whilst your site hosted in Europe, Asia Pacific or even your own country India. That distance does effects the website speed.