I know jack-shit about physics, so I googled this and got the following answers:
The main idea you need to understand is the concept of an equilibrium: a thermal equilibrium is achieved when the rate of emission and rate of absorption are matched. If we're not an at equilibrium, then the rates will be unbalanced; e.g. if the temperature of the surroundings is higher, then the rate of absorption of radiation will exceed the rate of emission, and eventually the black-body will achieve thermal equilibrium. But there is always this exchange going on.
Heat is energy, so when we say the black-body absorbs EMR, what we're really saying is that the black-body absorbs the energy of the EMR as heat. Oh, and a black-body is a perfect emitter in the sense that it absorbs EMR of all frequency perfectly; no EMR is reflected. Whenever a unit of EMR "touches" the black-body, it has 100% chance of having all of its energy absorbed in the form of heat and 0% chance of being reflected in another direction.
If no EMR falls on a black body, does it emit radiation? What you're asking is what would happen if a black-body is in a perfect vacuum with no source of EMR or anything - a complete, infinite void. Then the black-body will emit radiation IF it has any energy left. Eventually, the black-body will be devoid of any energy, like its surrounding void, and an equilibrium will be reached where the rate of emission trivially equals the rate of absorption - zero.
I hope this helps. I've not even kidding when I say I know nothing about physics; I did HSC physics, but I didn't even remember what a black-body is (or anything about it) until I saw this thread.
The most important part to remember about what a black-body is, is that it's an idealised concept - in other words, it's false and doesn't exist. It's just there because it makes the maths easier for physicists. So when you're thinking about black-bodies, don't fall into the trap of thinking that you're describing something that exists - it helps to know that you're talking about a hypothetical.