These sound like tantrums to me and I would just ignore her or make her go to another room if she wants to throw a fit over something like that. I think she will continue to do it as long as it gets her some attention. I'm not saying that she will stop altogether (although she might), but sending her to another room by herself should certainly shorten the length of these episodes since she won't want to be sitting in her room by herself. She won't have an audience there! When either of my kids pull these kinds of things with me, I just tell them that they have to go in their rooms (or timeout for my youngest) until they can settle down enough to talk to me without crying. My daughter is 4 and my son is almost 2.
Your daughter is plenty old enough to be able to talk to you without having, as you described, a "crying fit". I would start implementing some discipline in this area and see if it gets better. If not, then I might discuss it with the pediatrician because tantrums that escalate to that degree for such a long period of time don't seem normal for a 4 year old. But, if she hasn't been taught that this behavior won't be tolerated and that she won't get what she wants by acting this way, then you can't expect her to know any different. As for the paci, I say "to each his own", but you might want to think about taking that away sooner rather than later for a lot of reasons. I'm sure you've heard them, so I won't go there.....you didn't ask about that. :-)