Taking each question in turn ...
Is there a major difference in rate of change in MUAC for SAM versus MAM cases? Most of the work done on MUAC response has been with SAM cases. It would be simple enough to look at this in MAM cases using data collected in an SFP program. I can summarise what we know about MUAC response in SAM cases. There are three basic response patterns. We might call these "rapid", "logistic", and "slow". The "rapid" and "logistic" forms are very probably just examples of a typical "logistic" growth curve with the "rapid" form being seen because the patient is discharged prior to the growth / response plateau being evident. The "slow" response is a poor response and may be due to poor compliance (by clinic or beneficiary) or an underlying condition such as TB or HIV disease. MUAC and weight respond to treatment in very similar ways. Here is a chart (on its side to fit the EN-NET page layout) showing responses of three children in OTP:

Here are patient profiles for the three childen:
Rapid : Female; c. 42 months; admission MUAC = 10.5 cm; admission WHM = 67.4%; discharge MUAC = 13.5 cm; discharge WHM = 88.6%
Logistic :Female; c. 60 months; admission MUAC = 10.7 cm; admission WHM = 68.1%; discharge MUAC = 13.2 cm; discharge WHM = 89.8%
Slow : Female; c. 36 months; admission MUAC = 9.4 cm; admission WHM = 70.4%; discharge MUAC = 11.9 cm; discharge WHM = 90.8%
The presented data are courtesy of Save the Children (US).
There is, I think, no good reason to suppose that response of the MAM child will be much different from this (i.e. we will see a classical growth curve) although we might expect slower rates of gain in SFPs due to lower energy densities of the food given (an argument for RUSF), more inter-household sharing of porridge type products, and the absence of a systemic antimicrobial (which is also a growth promoter) in SFP protocols.
I think that response of the MAM child to treatment deserves further research and may lead to a revision of MAM protocols towards (e.g.) a lower intensity OTP protocol.
If MUAC cutoffs can be used for discharge in CMAM programs treating SAM, can MUAC effectively be used for discharge in any programming activities that are treating MAM/working to prevent SAM? I do not see why not. In SAM cases we are moving towards a MUAC >= 125 mm (for two consecutive visits) discharge threshold. Recent studies (in press) show (1) that this is a safe threshold for discharge in the sense that post-discharge relapse and death rates rates are below 5% and (2) discharging children before this is unsafe in the sense that relapse and death are more common in children with MUAC < 125 mm even if W/H targets are met. It seems to me that the same threshold could be used for MAM cases.
Or is MUAC not sensitive enough to be used in this way during recovery (specifically of MAM cases)? I think there may be issues with regard to monitoring visit-by-visit response as (1) we might expect slow rates of gain that would be masked by measurement error (i.e. there might be a 2 mm gain but this might not be detected) and (2) we might have a narrow window (i.e. cases would have a MUAC above 114 mm and below 125 mm). This does not prevent it's use for more coarse monitoring. For example:
MUAC > 125 mm for two visits -> Discharge
MUAC static for two visits -> Clinical check (refer if needed), counselling
MUAC dropping over tow visits -> Clinical check (refer if needed), counselling
MUAC < 115 mm -> Refer to OTP.
It may be advantageous to use a mixed MUAV and weight monitoring system as in:

This monitoring protocol is presented for illustration purposes only.
I hope that this is of some help.