When creating an updated version of a process, there are fields that I cannot change despite them being changed in the previous version. These fields are:

Process -> Objects -> Object Key -> Partition Association Mode
Process -> Finish Step -> Step ID
Process -> Finish Step -> Actions -> System Action Properties -> Action ID

I believe they can be changed via queries, but I've been unable to find anything about it in both CA PPM and the CA Support site.

Release: CODFSS99000-15.4.1-PPM SAAS FedRAMP-Sandbox-Small Environment
Component:

In terms of being able to update Process -> Objects -> Object Key -> Partition Association Mode the object that the process is based on needs to be associated to partition and in addition to that you (as a user modifying the process) need to be member of that partition.
In this particular scenario process is based on timesheet and timesheet is not an object that can be associated to partition so in UI you won't even get the option I being able to change it. The only way someone could have made this change would be through XOG.

For Process -> Finish Step -> Step ID
and Process -> Finish Step -> Actions -> System Action Properties -> Action ID, those are not to be changed after initial creation. The only way someone could have made this change would be through XOG.

As far is being able to change it via update database tables directly this is not something that should be done as it is not supported.