...heard that this is normal? Is this correct? Also, I'd like to know if it is ok to prune the 2 dead flowers, and just how low would I cut them ?

Seven years is longer than the average. When started from seed, they begin to bloom when they are about 4-5 years old--according to this article: http://www.bachmans.com/retail/tipsheets/indoor_plants/birdofparadise.cfm
Other sources say 3-5 years. This one had some additional info that may be helpful to you:
http://edis.ifas.ufl.edu/MG106
Yet, this one said 6 years:
http://www.post-gazette.com/homes/20010915quest0915fnp7.asp
Note: You can probably cut the dead blossoms off close to the main stem.