I can answer the "average" part. Here's a table from my usual go-to source for openly available Shuttle details, the Shuttle Crew Operations Manual, page 1009.
In this table, "PRCS" refers to the large Primary Reaction System jets, and "YRCS" is a typo for the smaller Vernier Reaction System jets. "NORM" and "LOW" are different settings on the Digital Autopilot. "FWD" and "AFT" refer to the different RCS pods in the Orbiter.
(The RCS system was divided up in two ways - a forward pod in the nose in front of the crew cabin, and aft pods located to the left and right of the vertical tail. Within each system, there were Primary thrusters (~900 lbs thrust) and Vernier thrusters (~25 lbs thrust). Each pod had an independent propellant system. The two aft pods could be interconnected, or cross-fed to the Orbital Manuevering System engines. There was no interconnect to the forward pod.)
So much for accelerations. For rates, everything depended on the Digital Autopilot settings, which were extremely flexible and reconfigurable, and therefore highly complex. The settings could be pre-loaded or changed by the crew in flight. Rotation rates and deadbands varied widely depending on mission phase, payload operations etc. Here are a few examples from the same source:
A7/VERN – Used for attitude hold (1 deg attitude deadband, 0.016
deg/sec rotation rate)
B7/PRI – Used for maneuvers (2 deg attitude deadband, 0.5 deg/sec
Re: the A7 and B7 nomenclature:
Each planned DAP configuration is given a reference number. In
general, the A configurations have larger deadbands and slower
maneuvering rates than the B configurations. The wider deadbands of
the A configurations are used to minimize fuel usage, while the
tighter deadbands of the B configurations allow greater precision in
executing maneuvers or holding attitude.
For some more detailed DAP settings, here are the tables for the last Shuttle mission, from the STS-135 Orbit Ops Flight Supplement. (starts on page 34)
Here's a brief writeup on the Orbital DAP. There's much more at the source.
The rotation rates and dead bands, translation rate and certain other
DAP options can be changed by the flight crew during the orbit phase
using the DAP CRT display. The flight crew can load the DAP with these
options in two ways: one option set may be accessed by depressing the
DAP A push button on the orbital DAP panel, the other by depressing
the DAP B push button. For convenience, each planned DAP configuration
is given a number and is referred to by that number and the DAP used
to access it. Typically, the DAP A configurations will have larger
dead bands and higher rates than the DAP B configurations. The wide
dead bands are used to minimize fuel usage, while the tight dead bands
allow greater precision in executing maneuvers or in holding attitude.
The RCS DAP can operate in both an automatic and a manual rotation
mode, depending on whether the flight crew selects the auto or man
push button light indicators on the orbital DAP panel. The manual mode
is also accessed when the RHC is moved out of its detent (neutral)
position. In both the automatic and manual modes, the rotation rate is
controlled by the selection of DAP A or B and the information loaded
in the DAP config display. In addition, in automatic, the DAP
determines the required attitude to be achieved from universal
pointing and then computes the RCS jet fire commands necessary to
achieve these requirements within the current set of dead bands. In
the manual rotation mode, the RCS DAP converts flight crew inputs with
any of the three RHCs to RCS jet fire commands, depending on whether
pulse, disc rate or accel is selected on the orbital DAP panel.
Simply, when pulse is selected, a single burst of jet fire is produced
with each RHC deflection. The resultant rotational rate is specified
on the DAP config display. When disc rate is selected, jet firings
continue to be made as long as the RHC is out of detent in order to
maintain the rotational rate specified on the DAP config display. When
accel is selected, continuous jet firings are made as long as the RHC
is out of detent.