Hello Elaine, I have put some answers below, hope they help
What does the check mark mean and how is it used? The data control field will be linked to a variable like any other data card control. The checkbox is used to control whether the variable has a value set or not.
How do I get a date control to be blank until a date is entered on a file card? I don't think you can get it to be completely blank. You can set the default value of the control to be "Text value".
How do I set a date to go in a variable as today's date automatically but still stays as today's date tomorrow and a user is not able to change the date later? You can set the value as today's date by default. If you make the control read-only, then users will not be able to modify it.
How do I set up a date so the user chooses a future date from a calendar and then it always stays as that date and a user is not able to change the date later? This is tougher. You can set the default value of the date control to be "text" so that the user can select a date. But you can't also have it read-only so the user cannot change the date later. A possibility may be to then move the file into a folder or workflow state where the user does not have permissions to check out the file and hence modify the data card.