Does 3NF require 2NF?
The normal forms are specified in such a way that for any normal form, the model is also meets the criteria for the lower numbered normal forms.  So, yes if your model is in 3rd normal form, it is also in 2nd normal form and 1st normal form. 

When normalizing a model, you normally work at resolving one normal form before the next.  This makes normalization simpler and less error prone as you are only applying a few rules at at time.  It is possible that an entity at a lower normal form is also at a higher normal form.  Most 3rd normal form entities are also in 4th and 5th normal form.   

4th, 5th, and 6th normal forms go beyond the functional dependence.  Where applicable, they further simplify the data, at the expense of more tables.  They reduce redundancy, and increase data integrity.