Any amp will power a 15" sub. What you need to know is what is the RMS of the 15" sub. Lets say its 200 watts RMS than you will want a max of 200 watts for your amp.
yes/no
Yes should be fine.
yes but the sound quality aint good enough :)
Technically, yes. Practically, no. Amplifiers and speakers are rated by the maximum amount of power (and at what impedance) they can handle. A 1200 watt amplifier will eventually destroy a 1000 watt speaker if it is operated at maximum power. In normal use, however, you rarely even get close to maximum rating.
A Rockford 250 watt amp would compliment a 12" Subwoofer very nicely.
For optimal performance, match the amplifier's power output to the rating of your subwoofer. The Rockford Fosgate 12" starts at a 150-Watt rating.
50 watts is a good amplifier size for use in the house. For other applications speakers usually have a power rating.
The Rockford Fosgate Punch 400-Watt Mult. offers a very good subwoofer output. You can also try the Boss CX1100M.
The MTX Audio Magnum MB212P 1000 Watt 2-12" Subwoofer Box w/Car Amplifier is a good one to start.
In watt watt watts
There is one currently available on Amazon for $15.43 which is decreased from $37.99. It is also the cheapest 8 inch subwoofer on there. It's called "Pyramid WH8 200 Watt High Power 8 Ohm".
Take a good 100 watt amplifier. Don't look for one with an output impedance of 4 ohms. All amps have output impedances of less than 0.5 ohms, because we use voltage bridging and not power matching.