Is there a way to reject time and expense entries, and have employees notified about the rejection?
Yes. From the relevant time and expense entry screens or Time & Expense Reviewer, you can review entries and then approve or reject them. Remember that un-approve is applicable to entries that are already approved. There is a separate Reject option. In the User Preferences screen, you can turn notifications on/off for the time and expense submit-approve workflow. This way you can be notified to submit or approve entries in CORE.
Similarly, you can be notified if your entries are approved or rejected. You can check the details, including the memo that describes the reason why an entry was rejected. Go to Time Entries > Detail for the rejected entry and check under Additional > Workflow. Check CORE Help Center for details.