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>1) determine the connection # of a remote view?
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You can use CURSORGETPROP( 'ConnectHandle')

>3) see total # of connections on SQL Server?

There is a screen in Enterprise Manager which will list all the connections and you can see which command was last processed. (well, you could in 6.5)

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>4) force a view to share a currently (manuall opened) connection ?

In the designer, I think there is Share Connection checkbox in the properties of the View, although I'm not sure how to do it programatically.

HTH