Explanation
Create a master-detail relationship field on Applicant__c to Application__c is what the app builder should recommend to meet the requirements of allowing the same applicant to apply for multiple open positions using a single application. This will create a many-to-many relationship between Applicant__c and Open_Position__c using Application__c as a junction object. Create a master-detail relationship on Open_Position__c to Application__c, create a master-detail relationship field on Application__c to Open_Position__c, and create a lookup relationship field on Applicant__c to Application__c are not valid or correct ways to create a many-to-many relationship.

The app builder should use Apex code to update a field on the parent record when a child record connected via lookup is deleted. Apex code is a programming language that allows developers to execute complex logic on the Salesforce platform. Apex code can be triggered by certain events, such as insert, update, delete, or undelete of records. In this case, the app builder can write an Apex trigger that runs after a child record is deleted and updates a field on the parent record accordingly. Option A, B, and D are not automation tools that can perform this task.