Hello, I checked the mentioned description of the project. Here are my views/clarifications.
1. Yes, I'll create custom component for you which show the catalog in categories.
2. In backend it will have categories display and edit page. Fields title, desc.
3. Products display and edit page. Fields title, desc, image, category etc
4. In frontend product list page and single product page.
Another common solution is using any existing component like virutemart which cost you $100 less.
I am okay with both options. Love to create new extension for you which actually will be cleaner to work on.
I’m glad to answer any questions you may have!
Thank you for your time,
Raj