use the API to integrate with the current login/reg flow with FusionAuth. This lets you keep your existing html pretty much untouched, you're just calling out to FusionAuth instead of the database.
remove them and use the FusionAuth provided pages with OIDC. This lets you use the theming and localization capabilities of FusionAuth, including super simple social signon.
It's your choice based on what your needs are, either way will work.
I'd only recommend using SAML if you have an application which only supports SAML, not OIDC.
You'll also want to make sure that when someone registers with one of your applications in FusionAuth, they register with all three. I'd probably use a webhook to ensure that.