If your meaning the cable is rated for 1200w and your hooking it to a 400w amp, then yes. Cables are sized by guage, the lower the number the big the diameter. A larger diameter wire will normally have less ohms, or amount of electrical resistance. Running wire rated for more than you need is always a good idea, this way your not putting too much power through a small cable ( you can burn the wire and everything touching it) or incase you want to upgrade later. And its always a good idea to put an inline fuse near your battery incase something bad happens, putting the fuse next to your amp in the trunk wont help.
You wont see any problem as far as the cable is concerned, as each device deteremines it's own resistance, and which will result in a specific amperage being drawn from the system (constant voltage), so no need to worry about that. The one issue you will want to address is making sure you reduce your fuse amperage. You want your fuses to be rated just over what you system should normally draw. Any more and your system might be damaged if it ever experiences a short, as your fuse might not respond as quickly as one with the correct rating. (There are several other reasons to use the correct fuse, but you get the idea, it's just safer and smarter) I'm assuming you are refering to 1200w Max power when referring to cable, which would probably be something like an 8Guage, hich probably has a 40Amp fuse, which is a pretty solid choice for a system under 500w (assuming you are referring again to max, not rms). You might want to swap it out for a 30 amp, thought, just to be on the safe side. If you are reffering to 1200w rms, then you have a 1 guage or so cable, and you probably have anywhere from 80-150 amp fuse using either Maxi or ANL fuses. If this is the case, that's fine, just make sure you switch out those fuses for the lowest ones you can get. I beleive ANL start at 100amps, but I think you can get maxi's as low as 60 amps. (Anything you need can be gotten at BestBuy, Circuit, or any local audio shops)
Yeah, the 1200w power rating means that that cable can handle up to 1200W so that's fine. As in the other answer the bigger the better, that means less resistance. hope this helps ya
Shouldn't be an issue. Just like an electrical outlet at home - it doesn't matter if you plug a microwave or a night-light. Both are handled without any issues.
Yes that is good the bigger your power cable the better. If it is bigger it will cause less resistance and energy will flow much more freely and this will mean your music will sound much clearer i personally run 1 guage to all my amps.