I'm having two problems with my new computer with Outlook 2013.
1. I can send email just fine the first time I connect to Outlook, but after that it doesn't work properly. When I first connect, it prompts me for my password and then sends the message as it should. However, on my desktop sending subsequent messages does not prompt me for my password again unless I close Outlook, but my laptop prompts me at least twice for every subsequent message. I'm using the same authentication on both computers now and that has not resolved the issue.
2. I have no problems deleting emails from the folder I've saved them in when those messages were received after I transferred my emails from my desktop to my laptop, but when I try to delete emails from before the transfer, Outlook says it has encountered errors in the data file and asks me if I want to run the repair tool. I ran it the first time, but when I tried it again, I got the same result. How do I fix this?
I assume you want to be asked for your password? How frequently are you checking for email? If under 10 minutes, authentication should be remembered. (The exact time may vary with mail servers, but 10 min is typical.)
On the pst problem, it errors on the computer that downloaded the messages? Have you tried repairing Outlook (in Control panel, programs and features).