If you don’t want to use the Wix Members app that is already provided to you through Wix Editor.
https://support.wix.com/en/site-members/setting-up-a-members-area
Then you can simply look at creating your own through code instead, here are a few examples.
https://support.wix.com/en/article/corvid-tutorial-building-your-own-members-area
https://support.wix.com/en/article/creating-custom-member-profile-pages
For passwords, that is all handled through Wix as we can’t currently make our own custom forgot password lightboxes, like we can do already with custom lightboxes for login and signup instead of using the Wix default or Wix custom form.
https://www.wix.com/corvid/reference/wix-users.html#promptForgotPassword
https://support.wix.com/en/article/site-members-password-retrieval