You most likely want to implement transaction control to ensure that all saves succeed or fail together. Here's a rough outline.

public class MyController {

  public ObjA recA { get; set; }
  public ObjB recB { get; set; }
  public Objc recc { get; set; }
  public ObjD recD { get; set; }
  public ObjE recE { get; set; }

  public MyController {
      // query and set recs
  }

  public PageReference saveAll() {
    // set a save point so that if one rec save
    // fails they all fail.
    Savepoint sp = Database.setSavepoint();

    try {
        upsert recE;

        // perhaps set the lookup field
        recD.recE__c = recE.Id;

        // save others
        // upsert, etc...
    } catch (Exception e) {
        // roll back if there is an error in saving
        // any of the records
        Database.rollback(sp);
        ApexPages.addMessages(e);
    }
    return null;
  }
}

What you've described is not a one-to-many relationship, but rather a many-to-many relationship (a Gym can have many members, and a member can be associated with many Gyms).

To capture this in Salesforce, you'll need 3 objects. You already have 2 objects, Gym__c and Member__c. The third object sounds like it'll be Membership__c.

This concept is called a junction table, though in Salesforce it's known as a Junction Object. Membership__c would have a relationship to both Gym__c and Member__c.

In the Salesforce documentation, they say to make Membership__c be the master in two Master-Detail relationships (Gym__c and Member__c being the 'detail' sides of those Master-Detail relationships). Based on you saying that a Gym can have 0 members, and a member can have 0 gyms, this would be a lookup relationship instead.

If you continue on reading through that documentation link, it goes on to say that you could include fields from Member__c in the related list on Gym__c (and vice versa), even though the related list is to Membership__c. You might only be able to do this if you make Master-Detail relationships though (I'm not able to test this out myself at the moment).

Adding multiple members to a gym sounds like a separate question to me. This question may be a good place to start