I don't know about your first question, but as for 2 and 3, yes. As long as each device supports MIDI in and MIDI out, they should be able to chain together appropriately. Double check with each device though, as some devices will process MIDI in instead of forwarding it.
But Ableton is really, REALLY good with MIDI. So as long as your daisy-chained ...
You will need a USB cable and some recording software.
There are several different types of USB cables as seen here
It looks to me that you need a type B on the drum end most likely a type A on the computer end.
Then you will need a midi capable recording program such as pro tools, finale, reason, etc.
Ableton Live and Max for Live could be used to do what you want to do.
You could filter out the midi data you don't want and then process the signals you want to use and manipulate them. The resulting data could then be routed to external midi devices, VSTs or used to trigger clips in Ableton.