Choose RV inverter: consider the batteries
Inverter size is measured in watts and should be large enough for the maximum combined power draw of your devices. There should be a watts rating plate on each appliance you have, so just add up those that can be running at the same time. Devices with motors or compressors may be rated in Volt-amps (VA). For estimating purposes add 10% to the VA rating and use that for the watts. For example, if the rating sticker says 200 VA, add 10% (20 VA) for a total of 220 watts.
Your microwave is the big power hog of the devices you mentioned, so a practical approach is to make the inverter large enough to handle the microwave and make sure the other devices are turned off for the brief time you will need to use the microwave. That allows you to buy a smaller inverter than otherwise necessary.
Your batteries are going to be the limiting factor in both amps and time. As the amp draw goes up, battery voltage falls and at some point the voltage will drop below the inverter’s minimum requirement (typically 10.5 dcv) and the inverter will shut off. The batteries also have to have enough stored energy to be able to sustain that amp rate for however long you need to run the devices, so you need enough amp-hours to last until you can recharge the batteries. An amp-hour is simply one amp for one hour, so a power draw of 100 amps for 0.5 hours is 50 amp-hours (AH). You can see that the microwave will quickly deplete even a large battery, whereas the DVD player uses very little AH.
A pair of typical RV batteries (Group 24 marine type) has an amp hour capacity of 170 when new and fully charged. After some use, this number usually decreases somewhat. In general you cannot use the full capacity without shortening the battery life, so the rule of thumb is to figure on 50% of the rated capacity. You can use 60-70% in a pinch, but if you do that often you will be buying new batteries fairly soon.
In practice I don’t think you will be able to run your microwave with just two batteries, at least not for more than a minute or two. The other devices should run nicely.
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