How to view a website containing Indic fonts in Android browser?
To answer the second part of your question first:

'Why does the previous solution only work on Firefox browser and not on other mobile browsers?'

You are using TTF file. This type of font file is supported by firefox , Safari and Chrome. The other browsers may not support it. For eg: IE supports EOT ; Opera supports SVG etc. But mostly all android browsers support TTF so that is strange.

In short check which type of font the browser supports.

'explain all the steps involved in the process of displaying the Indic font by Firefox browser'

In some scenarios, along with the web data, the web font is also embedded and sent to the browser which the browsers uses to display the data. In other scenarios, only web data is sent.The font used is not a web font (like in this case) In such cases the browsers searches for the font file within the system. If it finds it, it displays the data otherwise tries to display the data using some default font.