Animation exported from Blender, now how do I use it.

Hello everyone!
I'm quite new to unity and I'm not very experienced at blender either, and so I don't know what to do after I've made an animation in blender and exported it as .fbx file.
So, I've got everything ready, I suppose, but when I import it into unity, the animation isn't playing, I don't even know what to do next, as there's the rig, animation, color and other stuff, but why isn't it playing.
I'm sorry, I've just been trying to understand how does this work for some time now, and I just can't seem to understand, I've got a few other questions too:

If I model something in blender, and make animation for it, do I have to export it with the model and animation? (Just making sure)
So let's just say I somehow got Idle animation working, how do I add a different animation if I start to run, and to execute the running animation, do I need to write some lines of code for it to work?
Let's just say that I was running and I picked up a weapon, I'd want a different animation for it, but how do I model it and animate it?
I myself find this confusing, I doubt I explained my problems well, anyways, any response is greatly appreciated.
Also, a link to some kind of a full animation making, exporting, animation changing guide would be really helpful too.