Trade vetoes are also in place to prevent two teams trading together to build one great team unfairly. So one team could trade their good players to another for crappy players just to stack one team.
It keeps integrity intact.
There is only one draft. Then each week you set a new starting lineup with the players you drafted. You make adjustments for bye weeks, injuries, matchups, etc...
You can also "add/drop" which means you can pick up "free agents" (players who aren't currently on another league players fantasy team) from waivers. But, in order to pick somebody up, you have to drop a player from your team. At that point, anybody else can pick that player up for their team. So add/drop wisely.
There are also trades between other fantasy players in your league.
So say I had two QBs who both get injured...I don't like the available free agents, so I look at all your teams....maybe Ax has two good QBs...I might offer him a trade. Then he has to decline, accept or counter offer. So maybe start low and build up your offer as needed? But keep it realistic or it'll definitely be declined...