Is this a work email account? Are you using Exchange? In that case your
contacts and reminders are in that mailbox which is kept on the server.
There's no need to export/import with a PST. With an Exchange account, add
the PST to your account and you can drag and drop emails into it which
removes them from your Exchange mailbox. If you have a cap on your mailbox
this is one way to manage email though it's not optimal since the PST is not
backed up.
If you have a POP3 account, everything in Outlook from Outlook Today to
Tasks is contained in your PST file. This includes Contacts and the Calendar.
Please advise what type of mail account you have. Also, did you save off
your archive.PST or your outlook.PST? Outlook.PST is your default PST file,
or rather the name of your default PST file if you haven't renamed it.
Archive.PST is your archived email.
If you were using a tool to back up your PST file, did you ever verify your
backup?