OK, I've now managed to reset my iPad Air wifi only edition to iOS 9.1 via iTunes on an friend's Macbook Air, and then set it up manually as new, e.g. not from a backup. The whole point of doing this was to try to eliminate, or at least reduce, a number of bugs that had popped up after upgrading OTA from iOS 8.4 straight to iOS 9.1. The reverse has happened, I now have MORE BUGS AFTER REINSTALLING THAN BEFORE! How is that ACTUALLY possible?! As well as previously introduced Mail app bugs persisting, Notifications has now stopped working in it's entirety apparently, as well as having all sorts of problems when trying to define words in webpage text (usually doesn't work), or trying to highlight text and then perform other actions to that text.
On the original subject matter of the post, something interesting has happened, iTunes now appears to work with this iPad Air! I've done nothing to iTunes 12.1.3.6, but while as before it instantly froze on clicking the iPad symbol in iTunes after having connected the iPad, now it doesn't, suggesting a bug/incompatibility in iTunes and/or the previously updated version of iOS. So far I've been able to make an iTunes backup of the iPad and sync photos to it from the PC. Below are two of the problem reports logged by Windows Vista 32 bit at the exact times of the freezes, e.g. not the routine reports that you referenced every time I close iTunes. I've included two as the text in the reports is not identical, and I don't know how to read them;
Product
iTunes
Problem
Stopped responding and was closed
Date
31/10/2015 13:45
Status
Not Reported
Description
A problem caused this program to stop interacting with Windows.
Problem signature
Problem Event Name:AppHangB1
Application Name:iTunes.exe
Application Version:12.1.3.6
Application Timestamp:55f3f4a9
Hang Signature:b05f
Hang Type:2048
OS Version:6.0.6002.2.2.0.768.3
Locale ID:2057
Additional Hang Signature 1:adb3a541f9cc158154932ce4553179a6
Additional Hang Signature 2:1662
Additional Hang Signature 3:f2396469531c69cf2d7c7ed2adf944b6
Additional Hang Signature 4:b05f
Additional Hang Signature 5:adb3a541f9cc158154932ce4553179a6
Additional Hang Signature 6:1662
Additional Hang Signature 7:f2396469531c69cf2d7c7ed2adf944b6
Product
iTunes
Problem
Stopped responding and was closed
Date
31/10/2015 14:19
Status
Not Reported
Description
A problem caused this program to stop interacting with Windows.
Problem signature
Problem Event Name:AppHangB1
Application Name:iTunes.exe
Application Version:12.1.3.6
Application Timestamp:55f3f4a9
Hang Signature:f4c7
Hang Type:2048
OS Version:6.0.6002.2.2.0.768.3
Locale ID:2057
Additional Hang Signature 1:601c86aaf3d4e2127293c89f04e2bd59
Additional Hang Signature 2:0390
Additional Hang Signature 3:9e3ae7e6be6902175bdaedc635af4581
Additional Hang Signature 4:f4c7
Additional Hang Signature 5:601c86aaf3d4e2127293c89f04e2bd59
Additional Hang Signature 6:0390
Additional Hang Signature 7:9e3ae7e6be6902175bdaedc635af4581