Why Options A and C are the Correct Choice :

A. Custom Trigger on Custom_Team__c (The Mechanism):
Because the requirement specifies that the access level changes (Read Only vs. Read/Write) based on a data field value ("Primary" checkbox) and a specific user lookup, declarative sharing rules cannot be used. A trigger on the custom team object can dynamically insert, update, or delete records in the Loan__share table. If "Primary" is true, the trigger sets AccessLevel = 'Edit'; otherwise, it sets AccessLevel = 'Read'.

C. Apex Sharing Reasons on the Loan__c object (The Best Practice):
When writing Apex Managed Sharing for custom objects, you should define an Apex Sharing Reason (which populates the RowCause field on the share record). This is crucial because it prevents Salesforce from automatically wiping out your custom programmatic shares if the owner of the Loan__c record changes. It also explicitly documents why the user has access.

Why the Other Options are Incorrect
B. Criteria-Based Sharing Rule: Sharing rules can only share records with Public Groups, Roles, or Territories. They cannot dynamically look at a User Lookup field on a related record and share the record with that specific individual.

D. Owner-Based Sharing Rule on Custom Team: An owner-based sharing rule on the Custom_Team__c object will only grant access to the Custom Team record itself. It has no capability to look upward and grant access to the parent Loan__c record....

A. Create a custom trigger on the Custom Team object that inserts or updates records in the Loan_share object.
C. Create Apex Sharing Reasons on the Loan object to identify the reason the Loan record was share.

Custom Team object requires programmatic creation of share record on the Custom Loan Object (Loan_share).
Neither criteria based sharing rule or owner based sharing rule can be created on the go, there is also limit in terms of how many of these rules can be created per object.