They will likely waive your I-751 interview and you'll just do the N-400 test (I wouldn't even refer to it as interview because all I was asked were the civics test questions + quick reading & writing test, that's it).
It's 3 years (minus 90 days) after you received your GC, not wedding date. So count 3 years from May 2023.
Don't forget to remove conditions on your GC in the meantime.
I would start with following up with their office. Pester them if you need to.
My representative helped me tremendously when I reached out to them. Albeit they responded right away.
They can do it, and USCIS will respond to their inquiry.
If you apply ASAP, you might get all three visas in time for your trip.
I only have experience with French embassy, and it took about 10 business days to get my passport back.
I would stand behind this but only if USCIS spend that extra $$$ to significantly improve their website functionality. Because when I was doing online filing, it was a disaster.