Certified GKH Gardening Expert
You can prune some of the drooping branches, but it is best to do this during winter, when it is not actively growing. It will not hurt it to take off a few branches here and there, now, though.
I have addressed the grass seed question on the original.
This article will help: https://www.gardeningknowhow.com/ornamental/shrubs/holly/care-of-sky-pencil-holly.htm