Reminder: Update Your Domain Whois Info" and "Important Notice Regarding Your Domain Name(s)" are legitimate emails from Namecheap.com. These emails are simply a reminder to make sure your contact info is up-to-date.
Such notifications are sent from the <email@example.com> email, which is also legitimate.
If the contact information for your domain(s) needs to be updated, please do so from your Namecheap account.
Such emails are required by ICANN. You can also check more information about this here.