I plan to develop a web application that supports OpenID Connect as a relying party, so that a user of the application can sign up and log in using the identity provider of his
2. If I understood correctly, your use case is totally supported by OpenID Connect.
3. I recommend that you take look at IdentityServer3: https://github.com/IdentityServer/IdentityServer3 , as I am sure it will answer your requirements. I am using it personally and its great open source project maintained and developed by experts in the security domain.
Update:
I am not sure if you really require Dynamic Client Registration, in OIDC your whole application considered as single client/RP. your application clients/users (and set of users per each client of your application) is totally supported by most OIDC providers without requiring Dynamic Client Registration. you would need DCR if your application is umbrella of dynamic portals.