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Query1: Even though Right List Box is empty, "Move Up" and "Move Down" buttons are Active (On Initial Load)
We have checked your reported issue and we are unable to reproduce it in our end. We have prepared the sample for your reference, in this "Move Up" and "Move Down" buttons are disabled on Initial Load. Please refer the below sample link. If the issue still persist could you please replicate your issue in the below sample and send back to us, so that we can analyze and provide you a better solution.
Query2: When I move the Item from Left List Box to Right List Box, then focus should move to element of Right List Box. (Currently, this is not happening)
We would like to inform that it is a behaviour of our list box component. When move the items from left list box to right list box, we have set the focus on next item of moved item in left list box. Could you please let us know in which scenario, you set the focus on right list box?
Could you please check the above link and get back to us with more information if we misunderstood your requirement or need further assistance.