What *exactly* is electrical current, voltage, and resistance?

Before explaining current, we need to know what charge is, since current is the rate of flow of charge.

Charge is measured in coulombs. Each coulomb IS a large group of electrons: roughly 6.24 ˟ 10^18 of them.

The “rate of flow” of charge is simply charge/time and this calculation for a circuit gives you the number of coulombs that went past a point in a second. This is just what current is.

Resistance is a circuit’s resistance to current; it is, like you said, measured in ohms, but it is caused by the vibrations of atoms in a circuit's wire and components, which results in collisions with electrons, making charge passage difficult. This increases with an increase in temperature of the circuit, as the atoms of the circuit have more kinetic energy to vibrate with.

Voltage is the energy in joules per coulomb of electrons. This is shown though the equation E=QV where the ratio of Energy over charge= voltage. This is granted by the battery, which pushes coulombs of electrons, with what we call electromotive force. However when it is said that the potential difference across a component is X volts, it means that each coulomb is giving X joules of energy to that component.

Note: if an equation doesn’t make intuitive sense to you, chances are it is a complicated derivation, and to understand it you’ll have to learn its derivation.

In terms of circuits...

Current is the rate at which charge flows past a point in a circuit.

$$I=\frac{dQ}{dt}$$

The voltage between two points in a circuit is the negative of the line integral of the electric field along the circuit between those two points.

$$\Delta V_{AB}=-\int_A^B \mathbf{E}\cdot d\ell$$

The resistance of a segment of the circuit is the ratio of the voltage across that segment to the current through that segment.

$$R=\frac{V}{I}$$

The "concrete definition" you are looking for doesn't exist, and never will exist.

Physics isn't concerned about what anything is "really like", or "exactly" what it is. The answers to those questions are topics in philosophy and religion, not science, and are usually matters of dogma - which is "a principle or set of principles laid down by an authority as incontrovertibly true."

The only "final authority" in science is what you can measure, not what someone tells you.

The thing you should be concerned about is what "electricity" does, and not what it is. All you can ever "really know" about electrical charge is that it is a property of some things (like electrons and protons) and it comes in two "opposite" types, which we arbitrarily label "positive" and "negative". That's it. Sorry, but there isn't any more to know about "what charge really is". Everything else you will find in a physics textbook is describing what charge does, not what it is.

"Electric current" is just the movement of electrical charge. That sentence isn't quite as simple as it might appear. It does not say electric current is just the movement of charged particles, like electrons in a wire! "Electric charge" is not a "thing". It is a property of other things (like electrons).

In fact the previous paragraph isn't the whole story, because there are things that act like electric currents where nothing at all is physically moving. But understanding that in any detail will have to wait until you know enough math to handle Maxwell's equations...