Shoutbox

And as for to other things you mentionned: JSON and AJAX are not programming languages, they are simply 'modern' (and way to much hyped) acronyms or methods which indicate a typical use of a programming language, usually Javascript (but it doesn't need to be Javascript though. Those very same methods can be used in any programming language!)...
Can't explain it better atm, sorry. See Wikipedia for detailed explanation.

JSON (JavaScript Object Notation) is simply a data formatting syntax (like XML, or even plain text, etc). It is used to structure the returned data, comming from a call to a website, in a human readable form and yet easy to parse with programming without too much fuzz and extra and long winded libraries.

AJAX (Asynchronous Javascript And XML)) simply means using Javascript (or JScript, VBScript, or any other language tbh!) to post an asynchronous call to an URL, and maybe getting some data in return. This returned data doesn't need to be in XML formatting though.

AJAX is used all over the place. It's main use is to update websites with new info without reloading the page. eg: you clicking a button to update the weather info on a weather website without reloading the page. This is simply done by calling a Javascript function which posts a call to an URL. That URL will then return some data, the new forecast, in JSON format for example. That's "AJAX"... The Javascript function will then proceed in updating the HTML elements holding the forecast with the new info.

Without AJAX, stuff like Tweets on websites and such wouldn't be possible. That is: it would be possible, but it would require constant reloading of the entire website to see new Tweets... which would of course be über annoying...

But note that AJAX, JSON, and similar acronyms are nothing more than simple name inventions to give certain (very old) methods, which were already used looooong before those names were invented, a 'cool' name.

PS: in short, yes everything you said is possible. But no, you don't need to learn 5 languages... only the stuff NanaFreak said. Or... instead of PHP and MySQL, you could learn ASP/VBScript and use an Access Database, works just as well... It all depends on what you already know and what your host provides (and how much traffic you'd expect to get - if this is quite a lot (tens of thousands calls) then you better use a MySQL database instead of an Access database).