With regards to your question about whether Instragram users will be notified that they are blocked, the answer is No they will not.
If you block a user who is currently following you, you will notice that they are instantly removed from your followers list. If this user attempts to search for you, your username will not appear in their search. It will say "no user found."
When are blocked users on Instagram notified?
If the blocked user finds your account by way of seeing a comment you have made previously on another account, or simply typing your Instagram profile address into their browser, they will be able to see your profile picture followed by number of posts, followers and following, however it will say "no posts yet." This usually how a person can tell they have been blocked, since it appears to be similar to a private page, but a private page will clearly state "this user is private."
Also, if you click a profile that shows the user has uploaded a number of posts (eg 50), but specifies "no posts yet", this would inadvertently imply you have been blocked - since there clearly are posts!
So in answer to your question, while they will not be notified that they have been blocked, they may notice they are suddenly following one less user, and when they can not search for you, they may assume that they have been blocked. If they go to the extreme of finding your profile through other means, and see you have "no posts yet", they will certainly assume they have been blocked, and if they log out and check your profile and they can see everything, they will definitely know they have been blocked.
On the other hand, if they are not at all social media savvy, they may never know a thing.