I can't think of a reason why you'd see a discrepancy in the times between
how a message appears in the Inbox and in Advanced Search, but I'm running on
very few hours of sleep today.
On the other hand and on the topic of your first question, let's get the
obvious stuff out of the way...
- If you are on an Exchange server, do you have access to Outlook Web
Access? If yes, in OWA, do you see those messages you do not see in your
Inbox but do see when doing a search? If you're not on an Exchange server,
are you using IMAP and does your ISP provide webmail? See if you can locate
those messages in webmail.
- Do you see those "missing" messages in Safe Mode?
- What about if you create a new Outlook profile?
- Are you sure there is no filter on? The "Last Seven Days" view is a
frequent cause of such troubles...
- If you do not have a filter on, you could try starting Outlook with the
/cleanviews switch, keeping in mind that that will wipe out any custom views
you may have...