1. I can update a field name (in edit layout) and it is visible on the form view but the change is not reflected on the list view?
Any changes you make to label text in the layout should be visible in Form view and List view but will not be visible in Table View. To change the name seen in your column headings in Table View, enter Manage | Database | Fields and change the name of the field instead of just it's label text.
2. I can view a field I created (box names) on list view and then when I click on form view the box name field is empty! Why is this happening?
Hard to say. By "list view" I think you mean table view--judging by what you've asked in 1). Where in the layout is the field located? In the body? The Header?. In any case, in Form view, you may be seeing a different record than what was visible from table view where you can see many records at one time.
3. I want to link a "Box Number" field to a "Box Status" field so that when I identify the box status for one item, all the items in the same box reflect the updated status. Is that possible?
This requires creating a separate related table where you have a field for Box Number and a field for Box Status. You would put just one record for each "box number" value in this table. Relate it by Box Number and you can then add the Box Status field from this new table to your layout. Whenever you edit the box status for box number 1, every record in your original table that refers to box number 1 will automatically show the new status.
4. Is it possible to link a "box number" field with a "box name" field so that it is impossible to enter a box name with its associated box number incorrectly?
Again, this should be done in the related table I described in 4). Define your box name field in this related table instead of your current table. Then you can define a value list for your current table that lists box numbers and box names from the related table and you can add the box name field from the related table to your layout. When you select a box from the value list, the matching name appears on the layout.