Hi,
is there a way I can add to Garmin connect connection person without Garmin connect account? Or any other way I can share my updates with person not having Garmin Connect Account?
Yes. The easiest way would be to change your settings to make your activities public, and then give them a link to your recent activity rss feed or to your profile.
Your profile is at connect.garmin.com/.../<userName>, where <userName> is your Garmin Connect user name. Your rss feed is at connect.garmin.com/.../activities where <userName> is your Garmin Connect user name and <feedName> is the name you want the feed to appear as in a rss aggregator.
As an example, my profile is here and my rss is here.