What is the trend of basicity down the group and which is the better leaving group I(-ve) or Br(-ve) and why?

As Size Increases, Basicity Decreases
F>Cl>Br>I

Because when number of orbit reduces, attraction between nucleus and outermost orbit electron increases. This need more energy to get free electron from outer most orbit. This is why Florine (2 orbits) has higher basicity than chlorine (3 orbits) and other basic elements of that group.

Weak Bases are the Best Leaving Groups
As Size Increases, The Ability of the Leaving Group to Leave Increases: . If we move down the periodic table, size increases. With an increase in size, basicity decreases, and the ability of the leaving group to leave increases. The relationship among the following halogens, unlike the previous example, is true to what we will see in upcoming reaction mechanisms.

F<Cl<Br<I