How do I know it needs a rebuild and not just a resurface?
If the cracks are on the surface and the slab under them is sound, resurfacing is the right call and I will say so. A rebuild is for a crown that is split through, missing sections, or breaking apart in your hand, because a coating over that comes off with it. I photograph the top and send it to you, so you are not taking my word for the difference.
How long does the job take, and when can I use the fireplace again?
On a typical chimney the tear-off and the pour are usually a single day’s work, weather permitting. Concrete keeps curing after that, and it gets sealed once it has, so I will tell you on the day how long to leave it and when it is fine to burn again. Heat and humidity change that timing, so I would rather give you the real number that week than a number now.
Will a new crown stop my leak?
Only if the crown is where the water is getting in. The cap, the flashing at the roofline, open mortar joints and the brick face all put water in the same places, and a leak can come from any of them. If the photos show the water is coming from somewhere else, I will tell you that instead of selling you a crown you don’t need.