Correction: JavaScript embedded in web pages cannot process images. Mozilla Rhino most certainly can, and I'm pretty sure Mozilla SpiderMonkey can as well if given XPConnect (or similar).
The answer to the initial question, "Is Actionscript 3 a 'real' programming language?" depends entirely on who you're asking.
1) Flex application run in a sandbox, much as Java applets do. Locally, and currently, Flex applications can open files for parsing, but can not write to them. This is remedied with Apollo which is in alpha. Apollo is essentially a Flex application wrapper that provides a file system API, among other things.
2) This really becomes a question of whether or not someone is inclined enough to write the necessary Actionscript 3 as it supports binary sockets and byte arrays currently. Someone has already created a ZIP library.
3) Again, when Apollo launches, then yes. Although, a Flex application can run offline should it not require file system access, and even then files can be opened, just not written to.
Actionscript runs in a VM just as Java does, which is irrelevant given that the questions you're asking are entirely arbitrary. The answers to which only tangentially, and tenuously, provide support in defining whether or not a programming language is 'real'.
In the interests of providing my own answer... I would say no, it's not quite a 'real' programming language.
