Hello @Jorge Lee
As an Architect and Developer for my clients, I will answer the questions I am most familiar with.
1.) Typically the Zoning Dept./Building Dept. won't do this analysis. Most often this work is done by an Architect or Zoning Attroney, both whom are familiar with that locale.
2.) The cost difference is something you'll have to run the numbers for between a new build and rehabbing an existing property. Each market/location varies on construction materials and labor costs plus comparable available existing properties to buy.
3.) The amount of permits and how many plans, details and documents is totally under the purview of the Engineer themselves. Any professional (Architect or Engineer) will already know what is required based on their experience in that space. You shouldn't be trying to figure this out yourself nor is it very important. You hire them and they take care of this tasks which includes all the necessary documents and drawings to obtain the permits.
4.) Based on your questions above and this one, sounds like it would be beneficial for you to have an Architect on your team initially to go over all the processes for your build in your area. If you have no experience building or developing, hiring a GC is a toss up. They may be good or they may be not so good. You will not know if they're doing what they are supposed to be doing. An Architect can look out for your best interest in the project plus can bring all the Engineers necessary for the build (Civil, Structural, MEP, Sprinkler/Fire suppression, etc.)
As far as the build itself, if it's in an established city or town on a tax lot, then you'll need to go through the design and permitting process, gain zoning approval if necessary, and then build up from there. The details and logistics very much depends on what you are trying to build and how large.
I hope that helps.