Suppose A filed a provisional application yesterday. Today, B files an application that is very similar to A's, and says 'her' idea is unique and patent pending.
What happens is country specific. Most countries operate on a "first to file" basis, in the United States we have a "first to invent" rule. See First to file and first to invent.
In your question you did not say who was the first person to invent, A or B. In the USA the person who invented the product first should get the patent (assuming their application is correct etc.). First to invent is established by such things a lab notebooks documenting the invention and other evidence.
Of course in the USA the possibly exits that some third person, C, invented it before A or B and that C might file after both A & B filed and that C ends up getting the patent.
Here's my informal understanding - I'm sure an IP lawyer will correct any misunderstanding from my amateur observations.
Patenting is a winner takes all, first past the post system. The process of applying for a patent carries a risk (the details of your invention are made public), and a potential gain (on grant, no other party is allowed to use your invention without your agreement).
'Patent pending' is a signal that you have commenced the process, flagging up the risk to a third party that, should they duplicate your work and your patent be granted, you can go to law against them.
In your scenario, as far as I can see, all permutations are possible:
In sum, you can't do anything until you get an actual patent. A patent application, whether provisional or not, does not allow you to do anything.
n1. Will B get the benefits of her provisional patent?A patent application does not itself have any benefits so B does not have any actual benefits. Whether B can get a patent is somewhat complicated, but in a nutshell, B could only get a patent if it was the first to invent (note that US law will be different starting next year in this respect).
n2. Can A force B not to use the term 'patent pending' for the idea?No. As long as B has filed a patent application and the application is active, it can say 'patent pending'. Regardless, this is not something that you should be worrying about as claiming that something is patent pending provides no benefits.
n3. Can A cancel B's benefits about her provisional patent?No. That is up to the patent office. You can tell the patent office that your patent application is relevant to B's application but you cannot do anything else.
n4. If B tries to convert her provisional patent into a non-provisional patent earlier than A, can it be done without A's notice?Yes, but this is also something that you should not worry about since it doesn't matter whether B's application is provisional or not.