It is changing in general. Playing poker you want to change cards, you say io cambio. Driving the car, you can decide to change the gear (up or down), or your way instead of going for the usual way. It can be that you have decided to change your way to be. It is very generic here.
Of course, Stan! It's called "acento circunflexo" and gives a 'closed sound' or 'nasalized sound'.
The 'a' letter in English has the equivalent sounds, in Portuguese, of 'é', as in "cArry" or "blAdder"; 'á' as in "hOuse"; and 'â' as in "phAntom".
That 'nasalized' sound in "phAntom" is similar to the "cÂmbio" sound in Portuguese, a "closed 'â' ".
In Italian, the sound is like "cÁmbio" with an "open 'á' ".
I hope I can explain myself, since English is not my mother tongue...
No, this is not reflexive: "cambiarsi" means actively changing something about yourself, and it normally refers to changing clothes (really, other uses are rare or colloquial). "Cambiare" doesn't need an object: you change, matter of fact. In this particular sentence, out of context, it actually feels like there is an implied object, but it doesn't have to be so.