I had a Birthday Fastpass question I just posted myself.
It is not unlimited fastpasses. They divide the fastpass rides into two groups and they seem to allow for four fastpasses per person in each group. I say "seem" because I have also read of people getting 2 fastpasses per group per person.
There are threads about birthday fastpasses if you use the search function. I also googled "disney birthday fastpass" and found which rides were in which group for each park.
Sorry if this doesn't help much! I'm still figuring it out myself