To take control of the Downtown District you need to do the following!
complete all 16 activities
3 Tank Mayhem Missions
3 Insurance Fraud Missions
3 Trafficking Missions
3 Professor Genki SERC Missions
and 1 Guardian Angel Missions
Purchase all 10 Stores
2 Friendly Fire
2 Image As Designed
2 Planet Saints
2 Rusty Needles
2 Rim Jobs
Purchase all 8 Properties which are highlighted in orange
Defeat all 8 Gang Operations (there is 1 Gang Operation that is only reachable by air that's the one around the centre of the map around Loren Square for anyone confused)
( Also i wanted to say that if you cant find a gang operation if there is a grey highlighted on the map thats a undiscovered gang op littlebluetroll stated in a comment )
There is a Total Of 17 Collectibles to be found throughout downtown but purchasing the collectible finder upgrade will make it no problem!