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 🙂
Laura Solanes - Graphic Designer and Web Designer
Please be patient as I try to answer each topic as fast as i can.
If you like the theme or the support you've received please consider leaving us a review on Themeforest!
Always happy to help you 🙂