How do I make a custom shaped box?

In addition to the other suggestions, you could also use the bezier tool (the one that looks like a fountain pen). Once you've created the shape you want simply use select the shape and then "place" whatever image you want in the shape. All the autofit features will still work with the shape. Good luck.

Another option is to use the pen tool to add two poiints where you want the cutout to start, then use the direct select tool to select the bottom corner point and dratg it inward.

However you decide to creat the shape, Object > Corner Options... will allow you to round the corners. If you want all the corners rounded, do it after pathfinder operations. If you want to knock a square chunk out of a rounded corner frame, do the corners first.

Either use the Pathfinder tools to unite two rectangles, or just draw your custom rectangle with the pen tool.

You should check out a tool called Pathfinder (panel:Window>Object&Layout>Pathfinder or direct commands: Object>Patfinder)

With it you can add or substract different shapes... very usefull for everyone who wants to create new shapes in Indesign...