Well, since she's called the Headstrong Alchemist, yes, she's an Alchemist. 

Analysis is yeah, just like, in the midst of a stressful situation, she can generally keep calm and work quicker if not directly disturbed. Meaning of course, she'll still get put off of what she's doing if she gets actually hit. 

And the book is written by her, but everything is copied from other books, so she just copied everything she felt she needed into one single book rather than carrying a whole bunch around.