As i mentioned in the picture, my edit icon is not working (only for some post), but i am able to review and edit the posts.
Almost certainly there was a pending suggested edit on that post. I see in its timeline that a suggested edit was accepted 3 minutes ago. You don't have enough rep to approve the edit, so you don't see edit(1) as a prompt. There can't be two pending suggested edits at a time, so the edit option is disabled for you. It's possible if you mouse over it that you would be told about it. I can't be sure because I have too much rep to test it myself.