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.