Using a validation rule for each field that takes the Stage into consideration is the simplest approach to handle this new requirement. A validation rule can enforce the field requirements based on the logic and criteria that you define, and display an error message when users try to save a record that does not meet the requirements.
Updating the Opportunity page layout to mark these fields as required will not work because page layouts do not support conditional field requirements. Updating these Opportunity field definitions in Setup to be required will not work because it will apply to all stages and records. Writing an Apex trigger that checks each field when records are saved is not the simplest approach because it requires coding and testing

Using Bulk API to export 1 million records from Salesforce is the best option. Bulk API is a RESTful API that allows you to perform asynchronous operations on large sets of data. You can use Bulk API to create, update, delete, or query millions of records in batches. Bulk API is optimized for performance and scalability, and it can handle complex data loading scenarios.

The best solution to resolve the error of "Unable to lock a row" during the account load is to perform batch job in serial mode and reduce batch size. This is because roll-up summary fields are calculated synchronously when the parent record is updated, and asynchronously when the child record is updated. Therefore, updating many child records at once can cause locking issues on the parent record. To avoid this, it is recommended to use serial mode and smaller batch sizes when loading data using tools like Data Loader or Bulk API12.
Leverage data loader platform API to load data is not a good option because it does not specify the mode or batch size. Perform batch job in parallel mode and reduce batch size is not a good option because parallel mode can still cause locking issues even with smaller batches. Defer roll-up summary fields calculation during data migration is not a good option because it is not possible to defer or disable roll-up summary fields calculation