Trying to understand Battery Chargers
My assumptions were,

I considered the charger as voltage source
Battery also as a voltage source


Your 2nd assumption is more a less correct.
Your 1st assumptions is not entirely correct.  Li-ion1 chargers start with constant curent charging (charger is a current source), then switch to constant voltage charging.

(Source of the plot.  By the way, that entire site is an excellent resource on battery topics.)
Finally, I'd like to warn that you should be very careful with Li-ion batteries, because they catch fire when improperly charged (more on that here).  Consider a safer battery chemistry, for your introductory experiments.  Lead-acid or NiMH batteries are more abuse-tolerant and less risky.
1 Charging profile varies from one battery chemistry to another.
2 Related thread: Difference between controlled current and constant voltage charging