The whole point of using products like B2C is to offload your sign-in, signup, password-reset flows to another system which is tailored to handle it using standard protocols.
If you are looking for a streamlined way to integrate B2C login screens into your app, then take a look at embedded sign-in with iframe and it should allow you to embed a customized sign-in frame right into your app (this is currently only available via custom policies, not user flows).
As for API Connectors, they are used for process execution upon sign-up or sign-in, either as a part of token enrichment (i.e. grab more user related data from backend and insert in the token returned by B2C) or webhooks to execute another routine such as sending a welcome email or other type of integration.
If you want to do sign-ins that are purely executed from front-end form, you can look at B2C resource owner password credentials flow (ROPC) which is a very bad idea from a security perspective. It will also not help you in case of signup as this is merely a login mechanism.
However, if you want to use your own form to sign-up users, you're free to use the MS Graph API or any of the libraries which implement it.
Our recommendation is to use Azure AD B2C User Flows with redirects + optionally using API Connectors if necessary, and if you need embedded sign-in then instead use Azure AD B2C Journey Framing enabled Custom Policies + optionally using RESTful technical profile (which does the same thing as an API connector but for custom policies).