Very, very much location dependant. What makes you think that the roof, walls, siding and foundation are "intact" enough to rebuild? I would think you need to reach out to a local engineer, and contractors to get a true idea. And generally renovations are most often considerably more than new construction, so I would have to think it would not be cheaper. But as I said location dependant, geographically and propety wise.................

thank you, building new would be a better option, plus getting the house design I want

A fire damaged home would generally be a big turn-off for resale, even if you are ok with it. I say demolish and start new.

You need an engineer to look at the house. Depending on where the fire was concentrated, means there could be hidden damage. Example, the first floor collapses into the basement. The combination of intense heat coupled with rapid cooling(fire hose water) can weaken the foundation.

One point about remodeling/replacing, if the house is already bare to the studs, no repair necessary to the frame/roof, the labor cost will be similar to a new build. A large part of remodeling labor costs is demolition.

So, as long as the foundation/framing is sound, rebuilding costs will be similar to a new build. And, with design assistance from an architect, internal changes are possible.

It depends on the location. Take advice from a good engineer or your trusted architect. Did you claim for the insurance after the damage? Just visit a good public adjuster like Alliance public adjuster who will help you to get your insurance claim resolved. They will help you till the end and with all the engineers and architect provided by them.