If you would prefer to save yourself time and braincells, here is the short version of what they want to do: https://imgur.com/a/gSFoLZO
In this case I think they know this, but think it's worth it. If Trump died days before the convention, we probably end up with someone like Niki Haley with crazy good odds to become president. They would take that trade any day.
Yes photos are allowed, at least they were when I was there less than a decade ago. There is a whole bunch of politics over who runs things with the church specifically, because so many different denominations are involved, and when I was last there they even had to compromise and have the Armenians (there is a whole quarter in the old city for them) deal with opening and closing the doors. There are a lot of weird rules about who is allowed to do what that pertain to the church leadership and how its run, but people can just enter the church. Israelis have attacked people outside of the church, but that's not like a law, that's just Jews being assholes to Christians.
I have actually visited Israel before and been to both the Wall and the Church of the Holy Sepulcher. You can absolutely go inside, you can take pictures, and just like at the wall, there are places for prayers and photo ops, but they look much nicer because the Church is beautiful. Our rulers just don't care about Christianity as much as they care about the Jews.
She does, and thinks it's hilarious. These people are ontologically evil.