In answer to your first depends upon make and model.
There is no need for an external drum module when any half decent Arranger has hundreds of drum kit permutations and Styles available?
Or you can even create your drum pattern in the unit with whatever kit you want.
There are only two manufacturers that make effective Arrangers, Korg and Yamaha.
Watching the Tutorial videos ( not reviews ) produced by each company on whatever model is in your price range to get a better understanding of how they function.
To give an example in a Korg PA series ie 700/1000/4X you can create a MIDI file and edit it in the keyboard, there is no need for a DAW in a PC or MAC. The file can be exported as a MIDI or exported as an audio file.
So that is Question 2 answered
Additionally a MIDI file can be imported and played in an Arranger and it can also be converted into a Style, at least they can with a Korg.
Watch this series of videos.