Vertical cracks are fine, it's horizontal cracks you have to worry about. Those pictures look fine, you really want to see it from the side to make sure it's not bowing in or out, usually in from frost heaves from the ground or from heavy trucks in the driveway. Looks straight.
As for what to use, can't remember what's recommended, looks too fine for hydraulic cement. If it were just cement, some would say grind it out and pack it in. I'm sure a structural engineer would know what to use. Some lumber yards have them on staff and give free recommendations. That kind of a crack is overkill to consult a structural engineer though, see those all the time. Time to google it...