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1) Posts witch will be send by using the preview- or the the quick Reply Funktion have trouble to with german specific Ä / Ö / Ü, (Tested with Firefox)
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Do they not get posted at all, or do they result in some sort of an error?

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2) Who´s Online => in the Admin Panel Timeframe is set to 5, displayed is 10 Min.
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Does it actually state 10 minutes when looking at who's online? This comes directly from the config file. Do you have a URL I could look at?

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3) I´m not able (as Admin) to delete close an Topic.
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Things have changed a bit since the version you upgraded from. These are both done with the "Manage this thread" dropdown at the bottom of the page when viewing the topic.

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4) There is no calendar witch appears, neigther in Back- or Frontend.
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Is it just not showing in your menu? If you go to calendar.php does it come up at all

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5)I did not find the function to send a mail to my members?
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That is done with the Member Management tool in the admin area. Once you search for a set of users you'll then get an option to mail them.