What is the shortcut style of writing used by Indian English speakers called?

Solution 1:

It's commonly referred to as textspeak, or textese, among other terms.

Language regarded as characteristic of text messages, consisting of abbreviations, acronyms, initials, emoticons, etc. _(Oxford)

From Wikipedia:

SMS language or textese (also known as txt-speak, txtese, chatspeak, txt, txtspk, txtk, txto, texting language, txt lingo, SMSish, txtslang, txt talk) or "texting language" is a term for the abbreviations and slang commonly used with mobile phone text messaging, but sometimes used with other Internet-based communication such as email and instant messaging.

Three features of early mobile phone messaging encouraged users to use abbreviations: (a) Text entry was difficult, requiring multiple key presses on a small keypad to generate each letter; (b) Messages were limited to 160 characters; and (c) it made texting faster.

Once it became popular it took on a life of its own and was often used outside of its original context. At its peak, it was the cause of vigorous debate about its potentially detrimental effect on literacy, but with the advent of alphabetic keyboards on smartphones its use, and the controversies surrounding it, have receded and died off.

_{Emphasis mine}

Most of the things you mentioned can be chalked up to textspeak, inluding the lowercase letters and the absence of proper punctuation. They are just shortcuts Indians use frequently, but this practice certainly isn't exclusive to India, and it's not considered part of Indian English as far as I know. (I'm from India.)

In my experience, some Indian netizens simply don't realize that textspeak isn't proper in formal contexts. (This also applies to select contractions, like wanna.)

The overuse of sir is another matter. This is because of the tendency of Indians to convey respect, as they would in their first languages. It's a cultural thing. Indians usually address their superiors and teachers with some sign of verbal respect, and sir fills this void in English.

The various spellings you see is how they transliterate their pronunciation (which varies greatly from state to state in India). I'm afraid I'm not sure why they do that. If I could hazard a guess, it originated as a half-joke in informal circles.