Eat My Cake? SharePoint Search Folders

For what you are describing, you may just be able to use "regular" folders. You can propagate metadata using Column default value settings so that solves (1) and for (2), the answer is yes. You can use Content Types if each document has different properties or just add a column called Document Type if they all share the same properties (i.e. Client Name). When you create a folder for each Client Name, set a default in Library settings. This seems a lot simpler than using document sets. I would consider document sets if I have a library of JUST proposals so I can keep all the files associated with a proposal together and have a standard "set up" for each proposal set. But, for what you are describing, I would first try using a Folder per client AND a Site Column that you add to the library for Client Name.