BuddyPress.org

I’ve tried a fresh install of Buddypress with a standard wordpress theme and can’t replicate your issue.

The following code still works for both the bp legacy and bp nouveau templates.

add_filter( 'bp_activity_do_mentions', '__return_false' );

Perhaps you have something else bugging it somewhere in your theme or plugins.

Otherwise it might be best just hiding it through plain css for the time being, e.g.

.buddypress #activity-mentions-personal-li,
.buddypress #activity-mentions,
.buddypress .user-nicename {
	display:none!important
}

A similar concept in development cycle https://buddypress.trac.wordpress.org/ticket/8279

You’d have to ask your theme developer, Buddypress doesn’t have dark mode nor slideshow images.

Perhaps there’s something your theme hiding it or maybe you haven’t created the pages for the components yet?

Register and Activation Pages

The template you made overrides the current Buddypress one, this means whenever there’s an update to the buddypress template – best practice is to update yours accordingly as well.

That being said, there’s usually not that many changes made to the templates to keep it stringent.

That’s just how Buddypress works.

There’s conditions as to what is viewable whether or not if you’re logged in, or if its the user’s profile or not, due to security and privacy.

You’d most likely have to dig into bp_nouveau_get_nav_link() and see how you can filter it (if you’re on the Nouveau BP templates)

Do a quick search on the forum and you’ll find many other topics on this. Here’s an example

https://buddypress.org/support/topic/disabling-mentions/

Perhaps you’ll find your answer here

https://buddypress.org/support/topic/change-time-since-format/

https://gist.github.com/messaoudi-mounir/8706592

You can either find where the sidebar is being called in your theme, override the buddypress group templates to not have the sidebar or just hide it through plain css.

.buddypress.sd .sd-sidebar {
    display:none
}
.buddypress.sd .entry-content.sidebar-active {
    width: 100%;
}

I assume you’re talking about the group listing when referring to ‘clicking the group’. In that case I believe you’d want to customize the groups/groups-loop.php template by copying it into your own theme and conditionally remove the links if the current user isn’t a member.
Here’s docs on the template hierarchy in Buddypress – https://codex.buddypress.org/themes/theme-compatibility-1-7/template-hierarchy/

That should allow you to control that list of groups and suppress links depending on role.
As to the request access form if for some off chance they make it to that screen, if you want to suppress the form with a blocking message when they’re a member you can use the same template replacement concept to replace groups/single/home.php

Or potentially this plugin by @imath may be more appropriate as you could just make the groups private/hidden;
https://github.com/imath/altctrl-public-group

Please Login to your Dashboard and visit Appearance->Customize-> BuddyPress Nouveau -> Member Front Page.

Uncheck the option “Enable default front page for member profiles.” and publish. The home tab will be removed.

Regards
Brajesh