I think you will have trouble running a 1kW inverter from a few 5Ah batteries, the battery current capability will not supply the peak current of the inverter.
Similarly a few 5W panels are not going to run the inverter for many minutes a day.
Diodes will worsen the problem by adding a volt drop in addition to that caused by the limited battery capability. The inverter when connected and not running will store some charge in its input capacitors but the effect will not happen when running.
Try Amanda's tricks to make sure the meter is reading correctly but expect very low volts from those batteries driving a big inverter.
Flux
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