What you are looking to achieve using connected app is not possible. A connected app by definition is:
A connected app integrates an application with Salesforce using APIs. Connected apps use standard SAML and OAuth protocols to authenticate, provide single sign-on, and provide tokens for use with Salesforce APIs. In addition to standard OAuth capabilities, connected apps allow Salesforce admins to set various security policies and have explicit control over who can use the corresponding apps.
Even though you can connect to an app, you are still mapped to a profile as to what can you perform within the application after you are connected. To selectively provide access to say specific fields, you still need to control that using combination of profile/fls and permission sets.
As for multiple integration consumers, you will need to figure out what level of access is required by which consumer and accordingly setup their respective profile/users. You cannot have multiple integration consumers requiring different level of access mapped to a single user, they have to have different profiles setup or permission sets assigned for the purpose.