How do the team boosts work

As of patch 1.4 that went live on August 4th, 2017, there is now an option to modify build permissions from the menu, rather than going all the way to your Storm Shield.

Though not explicitly mentioned to you (and not exactly intuitive), giving your friends permission to build and gather resources in your storm shield defense missions is not in any of your typical menus. You can find the option in the storm shield generator itself, under the Permissions tab.

You can check each player's name individually to allow or disallow people from building onto* your fortress.

_{*read: "messing up"}

After doing some research (1, 2, 3), it appears that patrols are the purple glowy doors that appear at random and spawn a roaming group of monsters that run to another randomly spawned door.

Since I'd only tried using these traps in Stonewood, I didn't see a real difference, as these patrols were not exceptionally common. However, they occur much more frequently in Plankerton, especially while trying to build a fort around an objective. In most cases, the patrols attack unfinished structures and cause a bit of trouble.

This is what these traps are designed to prevent. By placing a Patrol Ward in or around your fort, it prevents these doors from spawning nearby and dropping a pack of monsters next to you. While not exceptionally helpful in Stonewood, they become much more important in Plankerton and beyond (so think twice before scrapbooking your schematics or trashing the ones you find!). However, these traps do not affect spawns related to the objective, so you can't use them to funnel monsters when defending.