Some masjids do, some don't. Those that don't ,women pray behind men as it's a man's job to lead in prayer.
For the most part there's no fukkery at masjids. It's mostly a place of prayer and if you disrespect it...well..
That said, there's internal debates. For example during Ramadan we have a mass prayer called Tarawih where we pray multiple prostrations in remembrance of God as we recite the Quran. During this, little kids that came with parents will often be in the back playing, wrestling, making noise. Some people hate this and find it distracting and the children need to settle, others say it comes with the territory.
The biggest drama that we have is about shoes. At the masjid you always take your shoes off. Some people take this as an opportunity to steal really good shoes but it rarely happens and most masjids have live feed security cameras due to Islamphobia so they're often caught. This is why many just go in sandals, aside from the convenience factor and not having to sit down and tie your shoes.
There is some slight racial tension. Most Muslim brothers are kind and treatment in kind if they're not black but others treat black people poorly and don't give salams back. That being said they're a vast, vast minority and I feel good attending pretty much any masjid.
Other than that, masjids are mostly drama free and spirit-filled. If you're interested, just go one day when there's no one there in like late afternoon after duhr or something and it's nice and empty and you can just feel Allah's love upon you and it draws you into a meditative state.
