When you unfollow someone on Instagram, you stop seeing their pictures in your feed. In order to see the pictures, you will have to follow them again.
The people you unfollow on Instagram can still see your posts normally provided that they are still following you.
When you unfollow someone on Instagram, they won't get notified, but if you follow them again, they will get a notification that you followed them. See what happens when you unfollow someone on Facebook.
When you unfollow someone on Instagram, their follower count will get reduced. If they already knew how many followers they had, they might conclude that someone unfollowed them. See also why do people unfollow you.
When you unfollow someone, you will also disappear from their followers list. If they check their followers list, they won't find you, and as a result, they might realize you unfollowed them.
The person you unfollowed can still message you normally. The messaging function doesn't get affected by the unfollow action.
If you unfollow a person then decide to follow them again, you will have to wait for their authorization if their account is private.
When you unfollow someone, your likes and comments will remain there and they won't disappear.