Outlook doesn`t receive Emails on certain accounts, nor sync or repair folder/account

Hello all together,

I´ve installed Outlook 2011 on an mid2011-iMac as well as on an 2013-MBA.

Both run OS X Mavericks 10.9.1.

With both Outlook-installations I experience the same situation:

- An Exchange Account is running smoothly. No problems.

- With to other accounts i have problems:

iCloud and web.de (German provider) accounts all connect to their servers (green signal as well as "connected with" in lower right hand corner). The respective folders are received and displayed in the sidebar. Therefore I must believe, that I´ve entered the right account informations and passwords.

BUT: NO EMAILS are downloaded or shown. Neither in the Inbox nor in any other folders. The "syncronize this folder" and the "repair this folder" commands don`t show any results whatsoever, either.

I can send emails from both accounts (iCloud and web.de). But the sent messages only appear for a really short time in the sent folders and then disappear.

After several hours of testing, searching the web and readjusting several setup-conditions, I have to give up and hope someone can help me.

Thx in advance.

Regards,

Alex