In the Dataform settings, you can set the activity to a daily interval. Then if you also set max entries to 1, this max will be applied to each internal. You may need to either limit entry editing time or deny updating an entry after submission. You will also have to deny students form deleting entries so that they don't delete the entries.
You don't need a time field to indicate the submission date. Each entry records the time it was created and modified. You can use the patterns ETM:timecreated and ETM:timemodified for display and for sort/search.
An alternate approach that is worth exploring, depending on the Dataform version you use, is to add all the target entries on behalf of the students via the csv import. You can import also the entry time created, so you can import "future" entries and restrict access to entries editing view with a filter that retrieves only the current day entry for each student.