I want to use a Lithium Ion Battery. I saw that there is also a different kind of chargers like Adafruit Micro Lipo/MicroUSB or Adafruit Micro USB Lipo for this kind of battery, do I need it? Can I charge my battery direct from a voltage source?
As mkeith mentioned in a comment, the charging starts out as CC (constant current) followed by CV (constant voltage). This is what the charging profile looks like:
The charging rate is noted as 1C, which just means the charge current is initially equal to the capacity of the battery for one hour, i.e. 1.5 A for a 1500 mAh battery.
If you are buying a stand-alone charger, then you need to buy one specially made for Li-Ion batteries, such as the ones you found. If you are building your own circuit to charge a Li-Ion battery, you need to buy a battery management IC.
There are not too many that come in hobbyist friendly through-hole packages. One that does is the BQ2000 which comes in an 8-pin DIP package. It automatically detects the battery chemistry, and will work with nickel cadmium (NiCd), nickel metal-hydride (NiMH), or lithium-ion (Li-Ion). It's available from Digi-Key for $3.46.
The answer is: yes, you should use a suitable battery charger. There are different issues regarding the safety of such batteries.
One is for example, the temperature control during charging. These batteries can explode if mishandling.