How did those dictionaries become the most respected like Webster's? Is it still profitable for them considering there is online dictionaries now? Also are different dictionaries more popular in other countries? Is there any non English dictionaries that are equivalent to Websters.
This sounds like something worth x-posting to /r/Linguistics - check with the mods whether it can be its own post, or a question in their stickied Q&A thread.
Dictionaries are descriptive. That means they describe how people actually use the words. If people are saying things like "totes", then "totes" goes into the dictionary if the editors so decide.
Since there is a huge amount of variety in English dialects, we then should expect to see a similar variety in dictionaries. Webster's is basically useless in England since it doesn't reflect their English.
The English language is really not very standardised. Instead of standards what youfind are conventions. Spelling still varies considerably from country to country, and even within a single country there is variability both regionally and on a person-to-person level. There is no official standard of English in America, for example. While most dictionaries for Americans will agree, this consensus is a matter of convention and not the result of any sort of national government oversight.
are different dictionaries more popular in other countries?
In Australia the Macquarie Dictionary is often considered the standard of Australian English spelling and usage, though like all dictionaries it's describing use and not telling people how things should be. Webster's has long been considered an ideal for American spelling and usage, but then in Canada you find the Canadian Oxford Dictionary. These three dictionaries will not agree on a large number of spellings or basic vocabulary. Your countertop is someone else's bench.
Webster's built a reputation early on and became a kind of standard in America, but the Oxford American Dictionary is going to have the same basic content. The reason again is because they're simply describing how the words are spelled and used. They're not saying how you should spell; just how most people do. That's also why they keep releasing new additions, because languages are constantly changing.
Is it still profitable for them considering there is online dictionaries now?
Most companies are also involved in online dictionaries, so this hasn't been much of an issue.
Is there any non English dictionaries that are equivalent to Websters.
Many major languages have reputable dictionaries that are taken as the standard for a given dialect, yes. The xiàndài hànyǔ guīfàn cídiǎn is often considered the standard dictionary for Chinese Mandarin, but then just like Webster's doesn't cover British English, the xiàndài hànyǔ guīfàn cídiǎn doesn't do you much good for Taiwanese Mandarin which differs considerably.