Explanation
Process Builder and Apex are two automation solutions that can meet the business requirements of summarizing the number of open and closed Cases related to an Account. Process Builder can create a process that updates the custom fields on Account based on changes in related Cases. Apex can write a trigger that performs the same logic using code. AppExchange and Workflow are not automation solutions for this requirement, but sources of apps or components and tools for creating workflow rules respectively.

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.