What is an amp (and other such basic questions) in the simplest possible terms?
An ampere is a measure of how many electrons move past a point every second (though technically, it's movement of any charged particles, but for metal wires it's always electrons).  1 ampere = 6,241,510,000,000,000,000 electrons per second.  A pipe with water moving through it could be measured in gallons per second.  Same idea.

Watts are not just used in electronics.  They're a measure of the rate at which energy is used or transferred.  A stick of dynamite and a candle have similar amounts of stored chemical energy, but the dynamite releases it much faster than the candle, so the dynamite has a higher power output (for a shorter time).  Likewise you could use two identical batteries in different ways.  If one way uses more power, the battery will not last as long.

1 horsepower is about 750 watts, if you're familiar with cars.  Just different ways to measure the same thing.

watts = volts * amps.  So a 60 W bulb plugged into a 120 V socket will be drawing 1/2 an amp.

60 W = 120 V * 0.5 A

In AC circuits, the electrons are vibrating back and forth instead of going in a continuous loop.  The frequency is just the number of vibrations per second.  50 Hz means they move back and forth 50 times per second.

It's important to understand the difference between current flow and energy flow, though.  The actual electrons in a wire don't move very fast.  In a DC circuit, the actual electron flow around the loop might be at the speed of molasses.  The reason flipping a switch causes the light to turn on very quickly is because the energy flow is very fast.  The energy is carried by waves in the electrons, not the electrons themselves.  They are constantly repelling each other, so when you push some extra electrons onto one end of a wire, the others nearby jump away, which causes more near them to jump away, and so on, creating a wave of "push" that travels down the wire and then pushes on things at the other end.  This wave travels from one end of the wire to the other at maybe 2/3 the speed of light, while the electrons themselves barely move.