Voltage vs current vs resistance – did I understand them right

Your basic misconception is that voltage is "supplying the electrons". The electrons (or whatever the charge carriers are in whatever material you are using) are always there. Voltage is the push to get them moving at the macro level. It is this motion that we call current.

Current therefore is a function of two things, how hard you push on the charge carriers and how much the material resists the movement of these carriers. Double the voltage, and you get double the current at the same resistance. Halve the resistance, and you get double the current at the same applied voltage.

In theory, the current would go infinite as the resistance becomes zero. In practise, the voltage source won't be able to support more than some current before it can no longer provide the voltage.

I'm guessing this is the phenomena you are imagining:

You hold the end of a garden hose with nothing attached, and turn on the spigot. Some water gushes out, with high volume, but low velocity. Then, you restrict the end of the hose with your thumb. The volume of the water is less, but the pressure in the hose rises, and it shoots much farther.

Hydraulic systems can make good analogies for electric systems. The problem is that not all hydraulic systems have an electric analog, and some people suck at making hydraulic analogies.

Here's one problem with mapping this hydraulic system to an electric system: charge is conserved, both in the universe as a whole, and practically speaking, most circuits. With your garden hose, an unlimited supply of water is magically created by the city water system, and when it exits the hose and hits the ground, it's no longer in the circuit.

To get the electric analog of this, you need a circuit capable of shooting charged particles out into space. You also need something capable of supplying charged particles. Things like this do exist (for example, a CRT flings electrons through a near vacuum at the phosphor coating on the screen) but they typically require high voltages, and you aren't going to build anything like this with just a resistor and a battery. If you connect a resistor across a battery, the electric charge is pumped around the circuit. No charge enters, and no charge leaves.

Another problem: very commonly, electric circuits are designed to maintain a constant voltage. The water supply system is also designed to maintain a (roughly) constant pressure. However, since nothing (electric or hydraulic) can supply unlimited current, all of these voltage/pressure regulation systems have limits. In the case of your garden hose, the water supply system can't supply enough water to keep the pressure at the end of the hose at the target, say 30 psi. With nothing attached to the hose, there isn't enough resistance for the supply to work against to build the pressure. It is analogous to an electric short circuit.

If you were to block the hose entirely, you would find the pressure inside the hose (and indeed, everywhere in your hydraulic system, if the hight differences are irrelevant) will be 30 psi. If you were to open the end just a little bit, you'd find that the pressure is still pretty much 30 psi. Only until quite a lot of water is flowing would the pressure drop from 30 psi; this is because at high currents, the friction of the water flowing in the hose becomes significant, and increasingly more of the pressure is lost over the hose's resistance as the current increases.

If we wanted to model the hose-thumb system electrically, we'd need to take into account that the hose has some friction. Maybe something like this:

^{simulate this circuit – Schematic created using CircuitLab}

This is called a voltage divider. When your finger is not on the hose, (\$0\Omega\$), the \$5\Omega\$ from the hose is very significant, since it's the biggest resistance in the system. When your finger is blocking most of the hose (let's say \$1000\Omega\$), then the additional \$5\Omega\$ from the hose makes very little difference.

but in a hose, decreasing the hose diameter (current) would increase the water pressure (voltage).

So with that explained, we can circle back to your confusion. It depends on where you measure the pressure. You probably know that if you totally block the hose, the water pressure does not rise without bound (your pipes would burst!). Using thinner or longer pipes actually decreases the water pressure available at the spigot (or appliance, or whatever is connected), because more pressure is lost to friction between the supply and the spigot. There's an electric analog: higher currents require fatter wire.