Why doesn't android studio show type of object or variables

It's ctrl + shift + p. You can customize it in File -> Settings -> Keymap -> View -> Expression Type.

One way I've found is simply placing the caret on the variable, and pressing F1. (Works with Flutter).

Alternatively, you can go to Settings->Editor->General and turn on Show quick documentation on mouse move.

In newer versions of android studio it is "Ctrl + Hover"

EDIT
On variable declaration line using "Ctrl + Hover" will show "Usages of variable".
On later usage of the variable it will show you its correct data type.