For a 700 watt load, an inverter rated at 1000 watts (continuous) ought to be very happy.
Let's do some easy math, using round numbers.
While producing 700 watts for the AC load, the inverter would probably take 800 watts DC from your batteries, the extra happening because the inverter is not 100% efficient when converting DC to AC.
So the current out of the batteries is 800 watts at 12 volts, or about 67 amps. Call it 70 amps for ease of arithmetic.
You asked about amp-hours of capacity that would be used. If you draw 70 amps from your battery for 4 minutes, your consumption will be 70 x 4 = 280 amp-minutes, or about 4.7 amp-hours. Just a tickle for your 200 amp-hour battery set.
Now, how long will it take to recharge the batteries? You are pulling 70 amps from the batteries. Your 300 watt panels will generate 300 / 12 = 25 amps at full illumination. But to be conservative, you might want to assume that they generate 15 amps in partial illumination. This number is subject to a bit of tweaking, depending on time of day, cloud cover, what kind of charge controller you get, and so forth. But the bottom line result won't be a lot different.
So if you take 70 amps out for 1 minute, you have to put 15 amps back in for 70 / 15 = 5 minutes, more or less. If you take 70 amps out for 4 minutes, you have to put 15 amps back for 20 minutes.
Yes, you have a very conservative plan for the microwave. However, the air conditioner is a much bigger load, and I don't believe you will get there with the system you describe. I'll let the experts chime in about this, as well as information about installation of the inverter and related parts.
One other thing. A cigarette lighter 12-volt outlet is rated to carry about 10 amps max, so it is of no use to you in this situation.
Bill
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