What sort of mode should be used on a Network Analyser for phase matching?
Should it be some sort of Time Domain Reflectometer mode?

Input impedance of network analyser is 50 ohms. Many cables are 75 ohms
impedance. For tests on these, a 75 ohm to 50 ohm converter or adaptor is
used. Adaptor name is something like 'min loss pad'.

My application is a system that checks the RF performance of a Unit Under
Test (UUT). The test cables that mate with the UUT are longer than the UUT,
so the aim is to get the cables to be exactly the same. This is reason for
phase and batch matching - to avoid differential error.

Because a lot of cables are analysed, the analysis is performed by computer
which connects to Network Analyser. What data sets e.g. S12 should be
compared by the Network Analyser to batch match the cables?

Cables have different connectors on end, but still have to be batch matched.
Have you any suggestions about this? Cables all have SMA connector at one
end. At other end, the connector can be 1) SMA 2) 50 ohm N type 3) coax
contact in circular connector.

Normally, phase matched cables are all made from same coax drum. Ensure coax
comes in on one big drum, not lots of small drums that may have been made at
different times using different processes (e.g. different operator or
machine setting).

Cables are batch matched and assembled. If several years later, a cable
breaks, how do I get a replacement batch matched cable to repair system?
Although, I would have kept spare cables from original build, the cables on
the system will have been subject to a different environment e.g. different
stresses and humidity.

Another scenario. RF cable is built in slightly more humid environment,
resulting in more moisture in dielectric. Vector gen run and passes. Cable
dries out becoming much better. Vector gen then fails. It appears that a
cable can become too good.