To your main question
The answer is no. You can not really "see" the very things that make up the cosmic realm of the microscopic regions. We use various methods to test the "reactionary likelihood" of certain theoritical constructs to see whether or not it is the case that certain notions, hold up to whatever degree they can. What this means is, that you must have a collected base of assumed notions about the overall nature of various concepts such as an electron, proton, photon, and the what not, and all these notions can with enough ingenuity be tested to a degree.
Take the following analogy: You are blind, hence, you really have no real sight of what distance is between one thing and an another. Saying so however does not mean, that you can't develop a theory "about what distance is" by doing somehting like, maybe finding a wall, and throwing a ball at it, to see if it makes a sound when it hits it, and to get a feel for how long it took for the ball to make the sound. You do this maybe with different object, at different measures that you may count with your steps, and "feeling" the differences in sound, and the what not. For example, you can feel with your hand the differences in texture between a rubber wall, and a brick, and associate these textures with what you have found about when you threw things against a wall. From this way of doing things, then, you can safely assume that something that feels rubbery seems to bounce, while something hard like a brick, just seems to hit the ground without any real bounces.
When you do something like this, you can inevitably develope your own theories that hold some kind of validity until you find something that invalidates your theories, or until new pieces of data arrives, that throws out of whack some aspect of your theories, thus requiring a slight modification of your theory to account for those factors that were not originally a part of the main theory/theories. A theory is technically a representative modal of something that you feel to somehow be an explantory answer to a particular question/equation. It is a sketch of a thought, a thought that seems to explain an observation, or experience.
When, we speak of gravity, and we think of Sir Isaac Newton, all that we are doing is using his modal of descriptive thought to account for why things seem to fall down when they are tossed into the air. His theory of how the size of an object seems to create a gravitational pull seems to explain then the idea for what is otherwise known as "gravity." But his theory in the strictest sense can not be proven to be true. It may vary well be the case that something else explains why things fall to the ground, and it has nothing to do with the size of an object which in turn may create a pulling force on another object that might be of a smaller size. But because his modal is better than nothing, we accept it as perhaps a valid description for why there is such things as "gravity." Theory of gravity then, is something that you can't really see, but you have notions that lend themselves to somekind of supportive base. Notions like motion, and how motion seems to be affected, and the what not.
In relation to atoms, electrons, and the what not, i think you have to get into chemstry, some math, and some physics, in order to create modals of predicability concerning "the nature of" certain elements. Once you develope these theories of the natures that govern various elements, you can then move on to creating the means necessary to justify the assumptions that you take as being descriptive modals for what something is.
To give you another analogy, let's say, you want to know if it is true that fire can burn things. Well, do that, you actually have to set certain things on fire in order to see the result. Based on your observations, you make generalisations, like water boils, at such and such a degree, or that it takes such, and such degree to melt metal.
When it comes to the microscopic realm, similar methods of testability is more or less applied. But over all, you can't really see the things you believe in when you get to the microscopic realm. You simply have to rely on guess work based upon what you already know so far about certain experiments. The theory of radioactivity, and magnetism must be variables to account for, and ultimately test, and fit into some aspects of your whole system of workable theories, or speculative modals.
