Some of my emails arrive and some do not in Outlook 2011

I've used Outlook for Small Business 2007 on my PC for several years and before that used Office with Outlook for many years before that.  Now I have an iMac.  I downloaded and purchased Office.  And I downloaded the trial version of Outlook 2011 (because it did not come with the Office purchase).  Some of my emails arrive and some do not.  That's the first problem.  Secondly, when the emails come in, they do not stay in my Inbox, but disappear a short time afterward and are in no other folder??  How can I keep this from occurring?  Thirdly, there are two folders under my Inbox.  One is my ISP and the other is On My Computer.  Why is this and how can I get just the Inbox to show?