crazy quilts are (usually) foundation pieced-
depending on the weight of the quilt top when finished batting is sometimes used- other times not.
since there is alot of embellishing/beads, buttons, ect...on a crazy quilt they are normally tied not quilted.
they do normally have a back.
some people work on embellishing one block at a time- others put their blocks together then embellish the quilt...and some people choose to machine quilt their crazy quilt- letting some of the quilting be some of the embellishment- then embellishing more after the quilting is done.
but traditionally- they are tied because of the danger of hitting the embellishments.