Voltage divider - Potential divider - it's all got potential to divide
Easy enough, example: 2 same value resistors, call them 1K, both in series, top of the stack to your input voltage which never goes above 10V, bottom of the stack to ground (which is also your PIC Vref-), middle of the stack goes to your A/D input on the PIC. If the input volts is 10V, the A/D input sees 5v (Kirchoff's Law simplified - the sum of the voltage drops in a circuit is equal to the applied voltage, you're splitting the voltage across 2 equal resistances. If the resistors were different, the voltage you would read at the A/D input would be a ratio of those 2 resistances).

Current sense resistor - yes, voltage 'developed' across the low value resistor would tell you how much current is going thru it, with just a little bit of math.
Would it work on A/C also? Sure...You could rectify, filter, and sample/smooth the input voltage and get the same thing as a DC input...or just do it all in software .

50W resistor - You're thinking about it backwards, go the other route with the number figuring. Yes, 50V @ 1A = 50W...but your sense resistor is usually on the order of .1ohm or less.
E = IR, P = EI, therefore P = IIR.
If you've got one amp, one squared = 1, .1ohm x 1 = .1W.
But throw in a bunch of fudge factor!