What are the "First Responder" and "Exit" boxes purpose in the storyboard editor?

Question 1

I've never used it and probably never will but you can assign an object to be the first in line to receive the events from the UI.

I suppose you could be creating a UIView subclass and add it in to a UIViewController but you actually want some other object to receive and process the events other than the UIViewController you are adding it to.

I found this link which kind of explains it a bit better.

Question 2

There are no good answer for this question, so I am posting my answer:

From here:

Note: You probably won’t be using the First Responder very much. This is a proxy object that refers to whatever object has first responder status at any given time. It was also present in your nibs and you probably never had a need to use it then either. As an example, you can hook up the Touch Up Inside event from a button to First Responder’s cut: selector. If at some point a text field has input focus then you can press that button to make the text field, which is now the first responder, cut its text to the pasteboard.

Edit:

1) First Responder is very useful if you are using text fields with keyboard notifications. I use it to make keyboard disappear, make an outlet to variable currentFirstResponder of your class, and in viewWillDisappear:

[self.currentFirstResponder resignFirstResponder];

2) You can read about unwind segues ("Exit" box) here

Question 3

First Responder: The First Responder icon stands for the object that the user is currently interacting with. When a user works with an iOS application, multiple objects could potentially respond to the various gestures or keystrokes that the user creates. The first responder is the object currently in control and interacting with the user. A text field that the user is typing into, for example, would be the first responder until the user moves to another field or control.

Exit: The Exit icon serves a very specific purpose that will come into play only in multiscene applications. When you are creating an app that moves the user between a series of screens, the Exit icon provides a visual means of jumping back to a previous screen. If you have built five scenes that link from one to another and you want to quickly return to the first scene from the fifth, you’ll link from the fifth scene to the first scene’s Exit icon.

More here

Question 4

You don't see this very often, where a deleted answer is actually correct, and the comment (likely influencing its deletion) on it is totally wrong! I'll try and improve on it.

Usually the IBAction you want to hook up to a button is in the view controller containing the button. However if the IBAction is in a different controller, e.g. a parent controller then drag from the button to the First Responder object and you are able to select the IBAction in the parent controller!

As the hidden answer states, how this is implemented is the action is sent to nil, which has the effect of the responder chain (i.e. view hierarchy) being searched for the action, as follows:

[UIApplication.sharedApplication sendAction:@selector(nextObject:) to:nil from:self forEvent:nil];

An example is a custom UITableViewCell. Add a UIButton to the cell but you want the action to go up to a View Controller that has an embed segue to a UITableViewController. Drag the touch up instead action to the First Responder and select the action in the container view controller. In the action to find the indexPath simply loop the visibleCells and check if the sender is isDescendantOfView:

- (IBAction)cellButtonTapped:(id)sender{
    for(UITableViewCell *cell in self.tableViewController.tableView.visibleCells){
        if([sender isDescendantOfView:cell]){
            NSIndexPath *indexPath = [self.tableViewController.tableView indexPathForCell:cell];
            NSLog(@"tapped %@", indexPath);
        }
    }
}

Another example could be a reload button: say your first view controller shows an downloaded item with an IBAction to reload it to get the latest data, then your child controller shows some detail, but you also want them to be able to reload the main item from within the detail, just add a button in the detail and drag its action to First Responder and select the reload IBAction in the parent controller. This allows you to hook up buttons to parent actions with no additional code like delegate methods!

For this to work the action needs to be in the responder chain hierarchy or it won't be found, you can read how the chain is built up in the docs. Also note if called from code the view needs to have appeared, viewWillAppear is too soon.