How can I set the tables in the cycle to display in an order different from the order in which they are calculated?
The field order in table versions in cycles is responsible for this.
It is taken when creating a cycle from calculation table versions.
How can I disable automatic table recalculation in the cycle?
This is handled by the automatic recalculation field in table versions in cycles.
It is taken when creating a cycle from calculation table versions. automatic recalculation
Can label fields address different places depending on the version?
No, they cannot.
How do I get the table version by code?
Take the code by cycle number and table name from table versions in cycles.
Where are the field display settings for the tables inside the cycle stored?
In fields_sets in version of calculation tables.