Как обработать нажатие на эту назад при открытой клавиатуре?

Надеюсь это тебе поможет

public static void hideKeyboard(Activity activity) {
InputMethodManager imm = (InputMethodManager) activity.getSystemService(Activity.INPUT_METHOD_SERVICE);
//Find the currently focused view, so we can grab the correct window token from it.
View view = activity.getCurrentFocus();
//If no view currently has focus, create a new one, just so we can grab a window token from it
if (view == null) {
    view = new View(activity);
}
imm.hideSoftInputFromWindow(view.getWindowToken(), 0);}

словить это событиие можно так:

@Override
public boolean onKeyDown(int keyCode, KeyEvent event) {
    if (keyCode == KeyEvent.KEYCODE_BACK) {

    }
    return super.onKeyDown(keyCode, event);
}