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;

https://www.2carpros.com/articles/engine-cranks-excessively-before-starting

https://www.2carpros.com/articles/engine-vibration-at-idle

https://www.2carpros.com/articles/engine-cranks-excessively-before-starting