Ohm's law ties together voltage (V, the push), current (I, the flow), and resistance (R, the opposition): V = I·R. Add power (P = V·I, in watts) and you have four quantities where knowing any two gives the other two. Pick your two knowns, type them in, and the rest fall out.
A 12 V supply across a 4 Ω resistor drives 3 A (12 ÷ 4) and dissipates 36 W (12 × 3). Double the resistance to 8 Ω and the current halves to 1.5 A — and the power drops to 18 W.
Put two 4 Ω resistors in series and you get 8 Ω; put them in parallel and you get 2 Ω. That's how you hit a resistance you don't have a single part for.
Whichever fits what you know: P = V·I, or P = I²·R, or P = V²/R.
They're all the same law rearranged. This tool computes all of them for you.
Parallel always lowers it (you're giving current more paths). Series always raises it. Two equal resistors in parallel give half; in series, double.
No — this is DC and pure resistance. AC adds reactance and phase from capacitors and inductors, where you'd work with impedance instead of plain resistance.
Power is heat. A resistor rated for ¼ W will burn out if you push 1 W through it, even if the resistance is "right." Always check the power against the component's rating.