I'm thinking that maybe there's something I can buy that has a charger port for the plug/connector in the picture.
(P.S.: If there's no such thing, pls tell me as I would just bring this to an electronic repair shop or something)

 

Is that lithium? I can't see the plug, but if you knew a little something about the battery itself, you could charge it using a decent bench power supply that has both a voltage limit and current limit adjustment. Or a more basic bench supply with a series resistor. Just figure out what chemistry it is, use that to figure out its current and voltage limits and be careful not to exceed them.

 

The battery has written on it "Lithium-Ion". I cannot read how many cells it has or its voltage.
It must be charged properly with a charger designed for it to prevent an explosion and fire.

 

That is a standard 18650 cell. Chargers for it are a dime a dozen. You would have to mate the connector to the charger though.