Call the maker and find out how that particular charger works. With four terminals, it COULD be just like a good OEM charger, which automatically throttles back and cannot overcharge an OEM battery for weeks on end.
Or, a cheap-*** charger, or battery, which has no thermal sensor and no charging control logic, can continue to apply a fast charge forever, which exceeds what any battery can withstand.
There's no way to know what you've got, except the general rule that no-name batteries and chargers usually are cheap for a reason.
On the second point, losing the charge in a month? Yeah, that's a sign of cheap-*** NiCad or NiMh batteries. The good ones (Panasonic, Eneloop, etc.) can hold 75% charge after a year on the shelf. Many brands will hold 50% for six months on the shelf. Cheapos? Dead in 30-90 days. All you can do with those is keep them in a trickle charger (even cheap ones should be able to take a 1/10C charge rate forever) or try to return them.
Personally I cringe whenever I have to replace batteries. The OEM ones are always ludicrous in price, and the aftermarket ones are counterfeit junk so much of the time that you really have to pick a supplier (like Bulldog Battery or the NiCad Lady, or a good commercial brand from Mouser or Digikey) and skip all of the "radio" second market as well as the unknown internet sources.