Francesco Corti is correct in that ADF is not the correct choice for this solution because at the current time it does not easily integrate into Alfresco Share nor doe it provide the components that you are looking for. Aikau does provide the components that you're looking for and is easily integrates with Share but only to work with existing Aikau pages or create new ones. As you rightly have pointed out the Advanced Search page is a very old page that is written in using Surf / YUI2.
This means that your options are either to take a copy of the existing advanced search code and update it with YUI2 code to fit your requirements (I wouldn't recommend this approach because you'll be using old technology and the solution won't be future proof against upgrades).
A better approach might be to look into replacing the page with Aikau. Unfortunately there is another issue here in that the advanced search page is driven by the Share forms runtime which is also tightly coupled with the YUI2 implementation. If you have a fixed design for advanced search (i.e just a single form for advanced search as opposed to swapping between forms when you choose a target content type) then you can completely forget about the forms runtime and build an Aikau form to submit your advanced search request - this would be fairly straightforward.
If you want to render different forms as defined in the Share forms runtime then you might want to use this experimental feature in the later Aikau releases which should be sufficient. Have a read through this blog post which although talks about inline advanced search the basic priniciples of using the Aikau forms runtime service remain the same (there are several other posts linked from that one that you should also read).
I don't believe that the underlying API will even support multiple content types however so your actual use case may not even be possible to implement - however I don't know for sure - I would definitely recommend trying to build out and test some requests (using something like Postman) to be sure that you can even achieve your goal before you start working on the UI.
If you go with the Aikau approach then you'll find lots of information in my blogs, a detailed getting started tutorial on the GitHub project, and lots of information on building forms in the video posts embedded in this post. You can also play with some Aikau widgets in the online sandpit and you'll find all the JSDoc online here.
