1. The first question is something that is not covered in the documentation because it’s not strictly something the plugin does. If you want to register your users so they can log in and have access privileges, you need to set them up with a WordPress account, Participants Database doesn’t normally provide that. If you have a situation where you have one Participants Database record per user, you can use the Participants Database User Profile add-on to automate this.
2. The plugin normally uses a “private link” which is a coded URL to allow the user to edit their record. The link is typically emailed to the user for them to use. If you want a simulated login that provides a way for them to enter credentials and gain access to their record, the Participant Login add-on does this. The is not a real login, so this is a completely different and separate way to control access to the record than I described in #1.
3. I’m not sure I understand what you’re looking for here. If you’re asking about moderating signups, read the section on Approving Records. You mention username and password…OK, that pertains to #1 or #2 above.
I know this seems a little complicated at first, but it is important to understand the plugin does not provide a login in the usual sense unless you use one of the two solutions described in #1 and #2. You can only use one or the other, not both. Use #1 if you want your users to be able to log in and have other access privileges on your site. Use #2 if you don’t need that, you just want to provide the user secure access to their record only.