You wouldn't be able to control the entire Ableton interface using the MPD32. That would only be achievable by using the Ableton Push or another controller that run around the same price such as the novation SLMK2.
That said, you should be able to assign the 6 parameters you listed ( sample itself, sample start time, sample end time, sample tune, sample volume, filter frequency) to a region on your controller (MPD32).
It looks like this controller has pads, faders, and turnable knobs that are assignable.
- Enable your controller as a control surface in your Ableton settings.
Here's a good article from Ableton's site that highlights the set up process:
Once set up accordingly, then there are several options to 'MIDI Map' those parameters to a region on your controller.
My recommendation is to import an instrument rack onto a midi track, and then load up sampler into that instrument rack. Assuming you have Ableton Live 9.5 suite, otherwise you can use the 'simpler' instead of 'sampler'.
The instrument rack will give you a macro box to control every setting that the sampler has, and you would simply "MIDI Map" the macro knobs to your controllers region.
Here's an article that explains the process above, and will show the sheer power of what Ableton's racks can do:
You could also throw a Sampler, Simpler, or any other Ableton instrument into a single cell of the drum rack.
Ableton's Drum Racks have macro's and act much like Instrument Racks do, but it's a little bloated to use a Drum Rack for this process if you'll only be using a single pad on the Drum Rack. To each their own, if you like the look of the Drum Rack, then go that rout :)
Set up the controller in Live's settings to send/receive and sync.
Nest the sampler device into an instrument rack.
Assign each parameter of the sampler you wish to tweak to a macro ( right click on the parameter in sampler and click 'assign to macro').
MIDI Map each assigned macro to a region (knob, fader, pad) on your controller. ( when in MIDI map mode - click the macro you wish to assign to controller and then press the area on controller you wish to be assigned ).