Repeting task with hotkey

Barb nailed it: a script can place a frame and apply an object style. Here's the script. Where it says 'xyz' enter the name of your object style.

(function () {
  try {
    var tf = app.selection[0].textFrames.add ({
      appliedObjectStyle: app.activeDocument.objectStyles.item ('xyz')
    });
    tf.insertionPoints[0].select();
  } catch (_) {
    alert ('Select an insertion point');
  }
}());

The anchored frame is inserted and the cursor is placed in the frame so you can type away straight away.

Apply the script to a shortcut key in the keyboard editor.

Hi @SuzzyFlamingo:

InDesign doesn't have macros/actions that you can record and assign to a hot key as you are describing. Someone with scripting knowledge can help with a script that will do this and I'll add the scripting tag to get their attention. 

In the meantime, without outside help (and a potential fee for development—it depends on who responds and the complexity of the job), you can create an object style for your text frame with your prefered settings. This will allow you to draw a text frame, drag to anchor it and then assign the object style (that can be assigned a keyboard shortuct!) with your frame presets.

See https://helpx.adobe.com/indesign/using/object-styles.html. 

~Barb