These are all good questions! Based on your description I assume you haven't had an introduction to solid state physics yet? Let's take your image of an electron that "jumps"
from atom to atom. In my understanding I wouln't describe it that way, to me it's a wavefunction of the electron that is almost independent from the valence electrons and you
can use the free electron gas approximation. Why is this band independent? See the following picture for an intuitive understanding how the atomic potentials define the possible energy levels within a periodic arrangement of atoms:
I think most of your questions will be easier to answer if you make yourself familiar with basic concepts and approximations people use to describe electrons in a solid first. Sure, a lot of things can be understood if we consider electrons to be little spheres that scatter from bigger spheres (ions), but you said you want to understand on the atomic level -> it's good to see the electron as a wave and see how this wave behaves in a lattice with certain boundary conditions.
First, I would read about a crystal. Atoms are arranged in a periodic lattice (assume a nice crystal for a first simple picture) and you can make assumptions based on this periodicity. You can define a unit cell and the Brillouin zone. You will see that the energy levels will sometimes split up in different bands and based on the filling of these bands you end up wih a metal, insulator etc. Electrons are fermions, can two electrons be in the same state? This defines the Fermi velocity.
This filling of the available energy levels describes the Fermi surface, a very useful tool
to describe other more advanced concepts. Then you will see what happens if you change the arrangements of the atoms or why in different spatial directions electrons can move due to the bonding of different atomic orbitals.
This could be a good start ; ) ->
http://britneyspears.ac/lasers.htm
There are other introductions out there, most of them describe the basics really well.
Electricity is the flow of positive or negative charges in response to electric forces (an electric field). Static means something is not moving, but there is still an electric field.
What is happening is normally positive and negative charges occur in equal amounts everywhere, so there is no net charge. We say they cancel each other out. If you have more of one or the other, then there is a net charge (an imbalance, as your text states). Since opposite charges attract, another charge would feel a force towards this imbalance. Similarly, the imbalanced charge would feel a force due to other charges surrounding it (ones that aren't cancelled out). If you live in a dry climate you may know the sensation of your hair standing on end after rubbing a balloon on it. What happens is each hair has some extra charge deposited on it, and all these charges are repelling eachother, taking your hair with it.
We say it's static because the charges can't go anywhere. This is because the extra charge displaces the charges nearby it, pulling the opposite ones closer and pushing the same ones farther away. What's important is that it can't push these other charges very far (the material is not a conductor). We say it "polarizes" the material.
Even though the net charge of one of your strands of hair might be negative, and be repelled by other strands, the extra electrons have surrounded themselves with positive charges and are "stuck" in a sense. This is why you need friction to cause an imbalance of charges. You are overcoming this stickiness.
Now if you brought a conductor (e.g., metal) to the material, the charge can attach itself to the metal in the same way, (polarizing the material and then pulling itself towards opposite charges) but because charges on conductors can move around, the extra charge can flow more freely. The charge is still "stuck" to the conductor, but can move around inside the conductor.
Best Answer
What we mean here by the word stationary is that the (macroscopic) charge density is constant , even if charges are moving actually.(An explanation for the word macroscopic comes in the next paragraph). A famous example is a rotating sphere with charge density $\rho$ , which is (electrically) equivalent to a non-rotating sphere.(But has a magnetic field due to it's current)
The point is that these models of matter are macroscopic models , which means that when we speak of charge we consider a big enough chunk of matter, much bigger than real charge carriers like electrons ( and yet small enough to consider variations of charge density in the matter). So it is correct that electrons spin around the nucleus , but the atom (or maybe some bigger group of atoms) as a whole is considered as a charge in our model.