Hello, for member name, fixed, please check attached 🙂
Your buddypress pages should be fine, also membership pages,
For the profile after login , try this plugin: https://es.wordpress.org/plugins/buddypress-login-redirect/
Users will be able to create groups at the groups page, also topics at the forums, but forums are only for admins at the backend.
To speed the site, check this http://seventhqueen.com/blog/code-snippets/the-definitive-wordpress-speed-guide-step-by-step-easy.html
I tried to update your plugins but your website was under a scheduled maintenance, update the theme required plugins please
Let me know if it helps 🙂
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