You didn't mention if that 1800W is Peak or RMS - I'll assume it's RMS.
(In case you don't know the difference: RMS is basically the power level it can handle all the time. Peak is the power level it can handle for a short period of time before damage potentially occurs. Usually, Peak is double the RMS rating.)
Many installers are comfortable recommending a 1 to 1 ratio. So, your 1800W sub would need an 1800W amp.
I don't feel that gives enough of a safety margin. I prefer a 1 to 1.3 ratio. In which case your 1800W sub would need a 2400W amp.
no you must go lower or the same
sure. Will it be loud? No. Its just not enough power to drive that sub.
4 gauge
yes it can
A #8 conductor is rated at 40 amps. Wattage is the product of amps x volts. As you can see the voltage is needed in this question to answer it. In the electrical trade I have never come across the terminology watt amp. Volt amp, yes.
a watt is power, or 1 joules sec= 1 watt an amp is 6.242 × 1018 electrons passing a given point each second,
Need to know the voltage the amp operates on.
To answer this question the amp hour rating of the battery is needed along with the voltage of the battery or bulb.
Yes, are we talking rms or max? If its rms you will have no problem. well the amp is a 1500 watt max but 350wx1 rms in 4 ohm
It's actually a good idea to have a speaker that can handle higher wattage than the amp can produce.
A minimum of 15-amp breaker is "needed", but a 20-amp is often required by electrical code for that situation.
1200 Watt wiring is more than enough for an 800 Watt amp. The rating of the sub doesn't make any difference to the cables. If you want to use the sub to its rated power you should get a bigger amp. If the amp can only give out 800 Watts and the sub can take 1100 Watts then you can put a bigger amp on. It is still going to be loud as with an 800 Watt amp. I have a 300 watt amp with a 1200 Watt sub and people hear me coming.