Is the EDMX file still needs to be generated?
I may misunderstand your question, but if you have the database created, and you want to access it using EF Database First technique, then you will need to generate the entity framework model(EDMX) in order to use EF to access the database. But you will generate it from the database. There is a model first technique, which is what you do NOT want to do.
There is another option, instead of using database first, you can use code first, and instead of generating an EDMX, you can generate the fluent mappings. Essentially reverse engineering the code first model. This is the only way I know of to use EF to access the database without EDMX.
Where should the entity conceptual models reside in my application architecture? Can I have all my models (DB models, view models) in a separate project?
I usually have my EF models(entity models), whether they are EDMX or Code first, in a class library. This allows me to reuse that library across projects that might access the same database.
My ViewModels go in the Models folder in the MVC project, since they are specific to the Views in the MVC project.
Alot of people have another layer that is usually classes that have functions like GetPerson, GetOrder, GetOrders, etc. that allow you to call and they handle querying the entity model, or perhaps return IQueryable that allows your MVC project to then add additional criteria. This layer may or may not also populate ViewModel's from the query. There are lots of variations. You can read up on "repository patterns". I personally would strongly recommend you not implement this layer until you have used EF and MVC for awhile. That way you begin to see what is redundant, or clutters up your controller, and this will help you gauge better what variation of the repository pattern you would like to use. It's difficult to adopt a pattern properly if you haven't experienced the problems it solves.