If I delete a picture in my photos will it also delete from the shared album?

The shared albums are holding their own copies of the shared photos. When you delete a photo from your Photos Library the shared version will remain in the Shared album. But the photos in the Shared albums may be in a lesser quality than the originals in Photos. All shared photos are optimized for sharing and will be scaled down to 20498 pixels at the longest edge and metadata will be removed for privacy reasons.

I recommend to save the original somewhere before you remove it from Photos if the image or video is important to you.