Moving username input and adding sections

Yes.

There are quite a few filter and action hooks in the plugin.

You can use wpmem_register_form_rows to re-order the array of form rows. You might be able to use that to slip in a heading, which you could also do with wpmem_register_form, which receives the entire form HTML as a string (that’s a little more cumbersome though).

The new user heading can be filtered with wpmem_register_heading.

That doesn’t sound like a WP-Members issue. I have had people ask about Yoast, and although not exactly the same as what you described, it is similar and the resolution sounds like upgrading PHP (https://wordpress.org/support/topic/fatal-error-cannot-call-overloaded-function-for-non-object-in-homehostpubli?replies=17).