Do cell phone batteries contain protection circuits?
Those batteries do have built-in protections, but not the kind of ones you see on sparkfun batteries.  They have thermal protection required for charging the battery and sometimes low charge cutout device which prevents discharging too much the battery.  However, there is no overcurrent protection, overvoltage and noob-proof abuse protections...

You have two pins for + and - (trivial) and a temperature pin to detect if the temperature rise is in normal levels.  This makes sure that the battery do not explode when charging it.  In practice, you read it as a variable resistance.  Some batteries also has a fourth pin tied to a voltage divider allowing the cellphone to detect the battery capacity.  If I remember well, Samsung is using such a thing to allow the cellphone's firmware to detect the capacity of the battery when there are many variants that could fit in the battery socket of the phone.  This feature is not used often, because they usually try to max out the capacity of the battery, especially with modern smartphone, but it wasn't so rare with old not-so-intelligent flip phones such as mine :)

Obviously, charging LiPo batteries is a risky thing if you don't have a proper setup.  Disclaimer: I do NOT recommend you charging your batteries without an approved charger.

That being said, one could charge it with any LiPo compatible charger.  Cell phone batteries typically have only one cell so it is pretty easy to recharge.  It should check the battery voltage and divide by 3.5 to 4.  This will indicate the amount of cells in series.  Then using a non balancing charger to recharge the cells to appropriate levels would work.  If charging the first time, one would hypothetically want to check with a multimeter if the batteries are getting hot with a remote circuit.  Also, that one might want to do that outside at a place where a battery catching fire or exploding would not hurt anyone around.

Seriously, just drop them to your nearest electronics store's recycling bin.  Its much safer.  You can buy cheap LiPOs at some RC hobby store such as Hobby King or whatever with an approved charger for like 30$.  It is really not worth the risks of injury.  Also if those batteries were taken out of a phone they are probably already at the end of their practical life, so...

Edit:

To complete on your question about your management IC: basically, yes you could use it.  It looks like it can charge up to 500mA, which is typical for cellphone batteries.  But... make sure to configure your IC to recharge at correct voltage levels, which may end up being trial and error since not all batteries are created at exact same target voltage.  If I were you, I would charge to one of the lower options first (4.35V or 4.4V maximum) and limit the charging to 7.5%-10% for the first one.  IF it goes well and the battery doesn't overheat, you can try other settings.  If it looks hot, revert back to a lower settings.  I ever saw a LiPo overcharging and while it didn't explode, gas formed and the battery inflated a little.  If you see the battery inflate, disconnect power and dispose of the battery. If you take great care and you know what you are doing, it looks ok.