You can enter future contests early. Just be sure to select the appropriate week from the drop-down menu when you do.

To address your first question, I'm not sure what you mean. Do you mean "submit another entry that is the same as a previous entry?" If so, yes, but keep in mind that judges are going to select based in part upon appropriateness to that particular contest. We do expect that you do some work on each day's prompt, though that's only tangentially related to contest entries.