Each MX Voice (there are no "patches") and each MX Performance has a unique "Bank Select" and "Program Change" number to recall it.

You will have to learn how to enter these into your MAINSTAGE device.

Each MX PERFORMANCE can recall sixteen Voices... One in each of a Performances 16 PARTs.
Each PART is on a separate MIDI Channel.
Each Part can be individually changed, as necessary. Or you can change the entire set of 16 by sending a message on the Basic Receive Channel.

For example. To recall Performance number 001 you would need to send:
MSB 63, LSB 80, Program Change 000

To recall Performance number 002 you would need to send:
MSB 63, LSB 80, Program Change 001

By recalling an entire Performance you can pre-determine what Voices are assigned to the 16 Parts in the MX itself.
If however you wish to change any of the individual Voices assigned to a particular PART, you can send a Bank Select and Program Change on the specific Channel of the Part you wish to change.

For example, to change the Voice in PART 1 of the currently selected Performance you can send a Bank Select number for each Preset bank, User Bank, Drum bank... Say you want to recall the Concert Grand in Part 1

MSB 63, LSB 000, Program Change 000

You can use the MX Data List booklet to see the Bank Select and Program Change (PC) number for each Voice... Often PC are listed starting from 000 and sometimes you will find them starting at 1, the MAINSTAGE will follow one or the other convention. Computers starting counting (quite properly) from zero, however, we humans usually do not... So be prepared to subtract 1 when calculating the PC number if the MAINSTAGE uses 000-127 rather than 1-128.

can one control the volume for each PART in a 16-part Performance using say a MIDI controller with faders?

I use mainstage too and can configure a midi controller comprised of sliders and knobs with eqch slider/knob assigned to any Midi Channel and send appropriate MIDI CC(is that what they are called?).

is this possible? one part with 16 independent part volumes?

Yes. One Performance with 16 Part Volumes, yes.

cc007 is main channel volume
cc011 is expression

You use cc007 to set the maximum volume for the channel. You can use cc011 to work within the maximum volume set by cc007.
cc007 sets the the mix balance - like when the program is recalled you can set a mix using cc007 on each channel 1-127.