Hi, quite a few questions and I suspect these could create many more!
The topics of dedicated circuits, high grade outlets and conditioners are all well documented here and really should apply equally in your scenario. The new item is of course the PV and storage battery.
One vision for renewable energy is for households to both create and store energy locally so that when combined with managed smart meters the grid may pay you for and call on the stored power to supplement main generation at peak times or when the renewable generation is low / varied. This would help smooth the flow of power round the country as needs and generation fluctuate. Your PV to battery to inverter solution would in this scenario be connected to the main supply at all times, meaning phasing and earthing would have to be maintained with the grid. Some suppliers already offer these solutions as off the shelf bolt on systems that literally plug in and go. Whether you run on battery, grid or part of each is unlikely to be your choice, your smart meter would decide for you.
In the case of a switch over system where at times you totally disconnect from the grid and run on local power (Either by choice or if the grid failed) then the provision of suitable earthing would be down to you. Power quality would be dependant on the inverter quality and earthing would need to follow the specifics laid down by the vendor. Such solutions are commonly used with backup generators though for a battery storage to provide this level of power you would need a very big battery!
If you’re thinking of designing something bespoke yourself then there’s a fair bit of research to do first, just thinking about this for 20 mins I’ve asked myself more questions than we started with! Have a look at Online Double Conversion UPS technology, a UPS of this type is designed to deal with the varied power inputs you may end up with and provide a stabilised sine wave output. Dirty AC voltage is rectified to DC then inverted back to AC cleanly. The DC bus can be fed from your battery or your rectified PV or grid or all combined.
Hope that helps a little