RSD is "Rapid Shutdown", PV module level electronics which disconnects each panel so a fireman won't encounter more than 80V within the array, 30V outside. In the US, I think it is required by recent versions of NEC, and each state adopts some version. For you, check with city permit office. But start by googling.
String inverters include SMA (they've discontinued PV only inverters in US, have a hybrid just now available.) Depending on what grid-support features, Rule-21, RSD, etc. are required, an older model may be acceptable.
Fronius, another premium brand.
EG4, GroWatt, probably more.
After you have grid tied PV, you may want battery backup. Maybe a hybrid inverter is the way to go. Or a separate battery inverter. Enphase offers their own (expensive) battery, but can work with battery or hybrid inverters including Schneider and SolArk.
Have you done the math comparing utility rates to PV, and considered what net metering plans are available, determined PV is a good investment?
Inverters are kW, not kWh. Batteries are kWh.
12 kWh/month / 30 days / 6 hours effective sun = 6.7 kW inverter suggested (check an insolation calculator, 6 hours is my location not yours.)
PV panels put out 75% to 85% of rating, so about 9kW of PV panels minimum.
Winter will be much worse. If you have net metering, oversize system so surplus in summer can provide credits meeting winter consumption.
A hybrid inverter like SolArk or Sunny Boy Smart Energy can process more PV than its AC capacity. So 12 to 15kW of PV panels on a 7.7 to 12kW inverter can be good.
You have an AC. How many kW does it draw running? Include air handler fan as well as compressor. What "LRA" or starting surge (about 5x running watts if not listed.) Inverter surge capability has to start motor.
Likely SMA SBSE won't do it, unless a small compressor. SolArk, Schneider, Midnight, some others are good at starting motors.
Inverter is 10kW, can produce 10kWh/hour, otherwise your math is correct.
String inverters and microinverters have MPPT function built in. So do hybrids.
Battery inverters like Midnight Rosie, SMA Sunny Island, Schneider don't have MPPT, can be used with MPPT SCC, those and some others can also AC couple to string inverters or microinverters.
My setup is older model Sunny Boy and Sunny Island. Works very well. Normally quite expensive, but old stock can be had cheaper. Only usable by you if your utility and city don't require some newer features.
SolArk is an all in one people are happy with, and fewer details to install.
Midnight is run by pioneers of the industry. Their Classic SCC is expensive but good. They just introduced Rosie inverter, not much history on it yet but it is powerful (can surge 15 or 20 kW). Midnight has an AIO, even newer.