Let me break your question down into separate parts to best answer each part of your question.
First and foremost, you DO NOT get an unlimited fast pass on your birthday. Disneyland does not offer any kind of fast pass on your birthday. In 2009 they ran a promotion called What Will You Celebrate that gave you free admission on your birthday and if you were an annual pass holder you would receive a special fast pass. The fast pass was sort of a waste, because there are not many rides at Disneyland that use fast pass. This promotion ended on December 31, 2009 and there is currently no type of unlimited fast pass promotion for your birthday.
The rides at Disneyland that have fast pass are:
Autopia, Big Thunder Mountain Railroad, Buzz Lightyear Astro Blasters, Indiana Jones Adventure, Roger Rabbit's Car Toon Spin, Space Mountain, and Splash Mountain.
The rides at Disney's California Adventure that have fast passes are:
California Screamin', Grizzly River Run, Mullhulland Madness, Soarin' Over California, and The Twilight Zone Tower Of Terror.
Having a fast pass does not let you "just walk onto rides". Instead, you have to go to the ride that you want to ride, insert your ticket into the machine, and a fast pass is printed out. That ticket has a return time on it. You then have to come back to that ride, during that exact window that is printed on the ticket to use the fast pass. Unfortunately, when it's hot and crowded you waste more time going back and forth due to fast passes then you do actually riding rides. Also, sometimes a fast pass wait turns out to be longer than the regular wait. I have seen people return to a twenty minute fast pass window, and the line for the regular wait turns out to be five or ten minutes.
Pirates of the Caribbean is not a fast pass ride and will not become one. Pirates of the Caribbean is one of the highest capacity rides at Disneyland, and even on an extremely crowded day the wait is 20 minutes or less. Pirates of the Caribbean makes the line move fast, and it does not take long to get to the front of the line. Haunted Mansion does have fast pass during the times that you mentioned, because it is transformed for the Halloween and Christmas seasons, and is considered a "special attraction". During that time (Halloween thru Christmas), the Haunted Mansion can see a line as long as 45 minutes or longer.
If you want short lines, go to your favorite rides first thing in the morning when the park opens and forget about fast passes. Save Pirates of the Caribbean and Haunted Mansion for during busier times or parades when the lines will be shorter. Pirates of the Caribbean is short all day but Haunted Mansion does get busy.