Custom app to Public app | Custom billing for Shopify app

[tech_dev]

Hi there, I have some queries related to shopify app.  
We have created a Shopify app which have theme app extension, it adds a button on product page which shows a iframe of our own website.
To distribute our app, we have two options, Public app and custom apps. 
Our target is public apps if our first merchant happy with it. 

So Initially we want to test it with one merchant only if it works well then we will be going with it. 
We are thinking to make a custom app first app then if all goes well we will make it public. 
Questions:
1. In partners website, when I select public app option and it asks for one time $99 fee, is it same for custom apps as well?
2. How to convert custom app into public apps, at various places it's written that we can't do that, but what if we create a new app with same code?  
3. We don't want to use shopify app's default billing system. We have our own billing system like our app can generate extra orders so we want to bill merchants based on number of orders. We want to do it outside of shopify's app store. We can manage it at our side. So is there any risk in that? Will shopify allow us for that? 
  
Thanks.