A: Yes, there is a red light near where the cord plugs into the light that should light up and indicate it is charging. If it doesn't, check the cord and if it still doesn't, possibly return it as defective.
A: If you have a converter. You can get standard European, etc. travel adapter kit to US 120 volt. Lots of people take things like hair dryers with them to countries using other types of outlets, and also take along the adapter. No US 240 to 120 though.
A: It uses a power cord with a figure 8 connector. It is also called a FIGURE 8 DOUBLE CIRCLE NEMA 1-15 C7 WITH LIP
A: This package has a recharegable cable for battery Not yet for a car charger cord.