Firstly, how many amps come out of a North American electrical outlet? I vaguely recall reading 20A but I'm not sure.

To power an electrolytic cell, can I take an extension cord, split the two wires and plug it into the wall as a power source? How likely am I to electrocute myself if i don't use some type of DC converter to lower the amps. Could I also restrict the Amps by using a power cord from say a printer, or VCR instead of an extension cord? they have Amp outputs anywhere from 0.1-1A.

It's limited to 20 amps after a short time. That's what circuit breakers are for. You could get more that 20 if you had a bigger circuit breaker...and didn't mind a possible fire starting inside your walls from weak wiring.

You don't want to use AC current...you need DC. You need current flow in a single direction. You can use one of those little DC converters from an appliance like you're saying. Although, if you draw too much current from them, they can overheat and destroy themselves, or worste, cause a fire. I think the current rating is more of a, you can get 0.1 amps at the rated volts...but if you try to draw more, the voltage will drop. although, in your case, that doesn't matter that much.

If you put the electrodes at a reasonable distance, you shouldn't overheat a common DC transformer. I like to use old computer power supplies. They are made to handle the load (5v at around 30 amps, 12v around 15 amps) and have all sorts of protective measures, plus active cooling

Just be carefull. NEVER PLAY WITH LIVE POWER MAIN VOLTAGES. It's too dangerouse, a stupid way to possibly die, and there's usually never a real purpose besides ignorance.

And, don't use table salt...you can make nasty chlorine gas that way.

Are you doing this just to make oxygen and hydrogen or something? Or making some rust?