May I draw rectangle by clicking three points in ArcMap
Yes, something similar is possible.
Set in the feature editing template the Default Tool to Rectangle
Don't expect equivalent functionality between different software packages. Tools are developed based upon demand, perhaps creating rectangles from 3 points is low on the list.
I can draw a rectangle by clicking three points in Microstation. May I do it similarly in ArcMap
You can accomplish this within an edit session. You just need to close the line or polygon after creating the 3rd vertex.
Introduction to the Editing Tutorial (Version 10.3.X)
http://desktop.arcgis.com/en/desktop/latest/manage-data/editing-fundamentals/introduction-to-the-editing-tutorial.htm
Editing Geodatabases Tutorial (9.3.X)
http://webhelp.esri.com/arcgisdesktop/9.3/index.cfm?TopicName=Editing_Geodatabases_Tutorial
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