Hello.

Reachmen have something against cities or they would have no problems to live in big cities? Example: After they have conquered skyrim (not take seriously)

and have the reachmen something against slavery?

I dont think they have an aversion towards slavery, and we know they live in big cities (Markarth used to be theirs)

We don't actually know a lot about the Reachmen

we only see the Forsworn, who we may surmise are Daedra worshiping Necromancers who indulge in human sacrifice - based on their rituals, their Hagravens, and the contents of their forts and camps.

The only notworthy thing about the native Reachmen who AREN'T foresworn are the facial tattoos.