I am giving you a walk through diagnostic for your hard start situation.
As far as the vibration it may be misfiring which I will also give you a walk though on or it could be bad motor mounts. Just use the links below to get to them;
Repair Safety Notice: This information is for general instructional purposes only. Vehicle repair can be dangerous. Verify all information, follow manufacturer service procedures, use proper tools and safety equipment, and consult a qualified repair shop when needed.