i would suggest downloading a version of it for quick reference. it's worth learning the commonly used functions, but a big chunk of php's value (and the main criticism against it) is a namespace filled with goodies (with varying degrees of good). This means there is probably a lot of useful functionality that's used sporadically enough that it's not worth committing permanent headspace to. Rather, learn to be quick about finding the right function to use. It's usually worth checking to see if there's some strange function/module that does exactly what you're trying to do. and if there's not, you can usually find example code in the comments - though i wouldn't recommend copying that code into production. rather, use it as a starting point for exploring the problem at hand.
i'd suggest learning php by giving yourself a well defined, if simple, project to start with and attacking it the same way you've learned languages in the past. probably with some reading, a lot of doing, occasional breaking, then more reading.
b) notepad++ or homesite are my preferred IDE's
c) codeigniter, cakephp ( http://cakephp.org/ ) and the zend framework ( http://framework.zend.com/ ) are the big frameworks i'm aware of, but i'm sure there are more out there.
enjoy!