Can I delete the video part of a Live Photo and just keep the photo?
Starting with iOS 9.3 and macOS El Capitan 10.11.4, Photos can strip the video portion of a Live Photo natively.


On your Mac, right-click the Live Photo, then Duplicate 1 Photo.  
On iOS, open the Share Sheet from your Live Photo, then tap Duplicate.


Select Duplicate as Still Photo, and you are then free to delete the original Live Photo.

You can even select multiple Live Photos and process them as a batch this way. This can prove especially useful starting with iOS 10.3 and macOS Sierra 10.12.4, which provide a new built-in smart album containing all your Live Photos. Simply go into Albums view and scroll down to Live Photos right below Selfies.