Are Anglicans considered protestants?
Depends on your definition. Our separation from Rome was certainly part of the breaking apart of the Western Church in the sixteenth century, and our 39 Articles are pretty clearly Protestant in their theology. However, because our version of Protestantism was fairly moderate, and because we have a wide range of doctrinal diversity, it is quite possible to be an Anglican without believing in any distinctively Protestant doctrine (in other words, one can be an Anglican and believe in the things that Catholics and Orthodox have in common over against Protestants–and many do).
Are they considered legitimate?
We are considered “legitimate” by Rome in the same way that other Protestants are–our baptisms are presumed valid (though at one time Rome was more dubious a out this) but our apostolic succession (and hence our Eucharists, ordinations, and sacramental absolutions) are not considered valid.
Since Rome made this determination in the late 19th century, bishops with apostolic succession have been involved in many Anglican consecrations, complicating the picture a bit. I refer you to GKC for more details.
I know at one point, because the bishops were legitimate, they were right?
Right. Under Henry, and even to a great extent under Edward, we certainly had apostolic succession.
Then the next generation of bishops or the next Archbishop would have not been.
Under Edward VI, a Protestant liturgy was adopted–and in the case of the rite of ordination, Pope Leo XIII in the late 19th century determined that the liturgy was defective in such a manner as to cause further ordinations to be invalid.
Do they talk about this stuff in RCIA? I start in a couple of weeks
It would depend on your RCIA program. I wouldn’t think it would generally be at the top of the agenda.
Edwin