BuddyPress.org

@sanz112
Short answer is you will need multiple plugins as well as some custom code to achieve your requirements. If you do enough research you may find the plugins and some code you can use to help in your endeavor on and off this forum. If you can’t write code or invest the time in doing the research to fulfill your requirements then you will most likely have to hire a developer by posting here:

BP Jobs Board

as well as here:
http://jobs.wordpress.net/
I wouldn’t make the mistake of posting an unpaid job on the latter link because I personally wouldn’t waste my time without being compensated for my work but maybe you may get lucky.
You also requested:

if u are not logged in u cannot see the platform.

I do offer premium plugins that can help with this aspect and if your interested you can inquire here:
Submit Comments, Tips or Tricks, or Job Inqueries
Good luck!

1.) For invites try: https://wordpress.org/plugins/wordpress-mu-secure-invites/
To keep logged out visitors from accessing BP pages check out: http://bphelpblog.wordpress.com/2014/09/27/private-bp-pages/
Usernames can’t be changed and if you don’t want users changing their password you would need to custom code it unless you can find a code snippet on the forum or on the net.
2.) You can use filters and you can also try this plugin: https://wordpress.org/plugins/bp-profile-search/
3.) Use bbPress: https://wordpress.org/plugins/bbpress/
You will have to search the plugins directory, the forums, and google the rest for your requirements unless someone else would like to take over where I left off. Hope this is at least a start. Good luck!