After consulting with my colleagues we need more information to be able to help you identify the problem with your boxwood hedge. Stippling patterns are usually made by spider mites, but spider mites usually first hatch in May.  The shower of white particles is reminiscent of psyllids, but the leaves don't show the normal pattern psyllids leave behind.

We would love to have close-up pictures of the leaves and the white particles in the webs of your first photograph, as well as photos further away.  Close-ups of the stems to look for other insects, and an overall shot of the hedge would be very helpful.   Normally, I would suggest bringing some of the material from the hedge to the Master Garderner Office, where they could examine it under magnification, but it's closed because of Covid.  Has this hedge shown any damage from excessive heat or drought?

Thank you for your help.  Working together, we should be able to figure out what is going on with your hedge.