WordPress Performance Engineer, WordCamp Speaker. All things Site Speed, Performance, and Multisite networks. Google my name for my videos, talks, and posts.
Yeah, technically it's possible. I can see the following scenario: the user installs the theme, after he activates it he is asked the company name and any data needed. Then this data is used to update the existing default data in theme files and database and voila, he gets the theme with data he provided. (or it can be fetched from the site name and domain name, of course)
I would recommend one of the Multilingual plugins for this (I use Polylang most of the times) if the content is the same for all languages and you need just translation.
But if you are thinking of having different websites targeting different markets I would use WordPress Multisite to build a network of websites.
It can be a network of subdomains for each language/country (en.site.com, es.site.com, de.site.com) or Top Level Domains (site.us, site.de, site.es etc).
Check out my talk about using WordPress Multisite for these types of cases https://sabrinazeidan.com/wordcamp-london-2018/ (Starting 20:41 in this video)
This might not be the main reason for your website positions going down, but it's something that will keep you from going up. Most of your visitors are from India, if you test a website speed for mobile users (with fast 3G connection) from India you'll see that it's rather slow https://webpagetest.org/result/191225_WA_972a2ca7545ba636e9a31c2dc3f0f7f3/ Site speed continuousely stated by Google as an important ranking factor that you definitely would take into consideration. You should aim to make your SpeedIndex at least twice better to rank high in Google (now it's 2.9s for the homepage). More information can be found here https://sabrinazeidan.com/tag/site-speed/