Your side walk, in your climate, is a very poor candidate for a fast and easy repair (such as a skim coat). Too many cracks and problems, meaning all will reflect up through whatever you add to the surface. And probably debond after the first year, putting you right back where you're at right now.
As a first-time concrete placement, this could prove to be challenging for you. Especially at this time of the year, when the frozen concrete (resulting from improper preventive measures being taken) will instantly ruin the job, and you'll again be back where you started. Wait until Spring, or do it using pavers instead of concrete if you absolutely have to do it before the snow flies. If it was mine, the new walk would be curved, to go around that raised slab on the left, and provide some artistic appeal.