Most thin or topped shots are not caused by picking your head up, as commonly believed, but rather because your muscles tense up and shorten the distance from your club to the ground
Working on your swing in slow motion will allow you to analyze what you are doing on each part of the swing, which will help you fix your flaws but also get away from swinging segmentally
When just off the green you can either putt through the fringe or chip using one of these two chipping techniques, don't just do one, try all three and use the one that you are most comfortable with