Hi there and welcome to the forums!
I think you can expect to ask for a D3100 battery at your local camerashop and you would get one, but in case they don't know which is the battery, ask for the Nikon EN-EL14 battery, this is the Nikon battery for the D3100.
By the way, not all Nikon batteries are compatible with all the Nikon DSLRs.
Also, a fully charged battery should not discharge while not in use, because it won't be a really long time, as long as it is not in the camera, you can expect it to be fully charged when it's ready to use.
I hope I helped
