Can the arduino alone act as a web server taking serial commands from the client without any intermediate computer acting as server?
Yes, it can. Works great.
Can the arduino handle camera feed if used directly instead of a computer acting as server?
"Handle" is such a vague term. The Arduino as a web server can not stream video data, It is far to slow for that. It can serve up a page that includes a frame where the web cam data can be shown, if the camera in question is a web cam with it's own web server setup.
From what I have seen in the forum and other places, PHP seems to be apt for this purpose. I will have to learn PHP as I have not really done any web programming before. Can you suggest any books that you think are good?
PHP is easy to learn. It is based on C. php.net
has a link to the documentation. There are tons of examples provided there, and in other sites on the web.
This is all academic, though, as the web server that you are trying to program is the Arduino, and it can not do PHP processing.
And any suggestions regarding whether any other language should be used instead?
For what? Basic html is all you need to understand, because that is all the Arduino can serve up.