Soldato
You're head has every right to hurt, there is lot to understand, a lot of misinformation out there, a lot of outdated information, and a lot a useful info, but sorting the useful from the not so useful is hard work.Looking at 2 x 5.2kwh storage batteries so that we can charge one whilst using the other to power the house.
Firstly what you describe in the bit above (that I've quoted) is not how it works, batteries are either charging, discharging or doing nothing, you can't really have one charging and one discharging, two batteries might balance to each other but we'll ignore that as that's not what you're talking about and really irrelevant.
If you have solar power, then firstly the house is supplied, and any excess will go to the batteries, and once they are full any excess will go to the grid, up to your permitted export power.
When the sun goes down or behind clouds the batteries will then supply power, once the batteries run out, the grid supplies power, all this is done automatically.
A lot of people, especially in the winter will charge off peak overnight, so if the sun isn't shining they run on cheaper off peak electricity. What catches a lot of people out, is their inverter isn't powerful enough to fully charge the batteries in the off peak period.
Another thing you need to be aware of, is getting paid for your exports (you're a low user so in the summer you will export lots with 20 panels), to make life easy you need an MCS certificate, otherwise most energy companies won't pay you. Octopus have been trialing a non MCS thing, but its very hard by all accounts to get onto it, and very little information.
When you say inlayed panels, what you are referring to what is known as in roof installation, where your roof tiles are removed, trays are then fitted in the roof and the panels installed in them.
One company that keeps coming up on here with good reviews is Spectra Solar, they are based in Wigan, but cover quite a large area, perhaps give them a ring.